Arabian Journal for Science and Engineering https://doi.org/10.1007/s13369-023-07642-x RESEARCH ARTICLE-MECHANICAL ENGINEERING Optimization of Cutting Parameters and Result Predictions with Response Surface Methodology, Individual and Ensemble Machine Learning Algorithms in End Milling of AISI 321 Deniz Demircioglu Diren1 · Neslihan Ozsoy2 · Murat Ozsoy2 · Huseyin Pehlivan2 Received: 25 July 2022 / Accepted: 18 January 2023 © King Fahd University of Petroleum & Minerals 2023 Abstract Optimizing the parameters in the milling method is important in terms of cost, energy, and time. The forces that arise during milling cause undesirable results, such as tool wear and energy loss. In this study, cutting parameters were optimized during the milling of AISI 321 material. Cutting speed (60, 70, 80 m/min), feed per tooth (0.04, 0.05, 0.06 mm/tooth), and depth of cut (0.25, 0.5, 0.75 mm) were selected as input parameters. Cutting force in the X and Y axes and the surface roughness were selected as the output parameters. Optimum parameters (60.80 m/min for cutting speed, 0.04 mm/tooth for feed per tooth, and 0.25 mm for depth of cut) were found using response surface methodology. The effect of cutting parameters was calculated by analysis of variance. The most influential parameters were found, depth of cut as 87.49% for cutting force on the X-axis, 86.48% on the Y -axis, and for surface roughness, the cutting speed with 36.48%. Prediction models are compared to choose the best model. Individual (Neural network, decision tree, and k-nearest neighbor algorithms) and ensemble methods (vote) from machine learning and response surface methodology from statistical methods were used for models. The error rates of the models were compared according to the mean absolute percentage error performance criterion. The lowest MAPE values were obtained with the vote method 11.163% in the X-axis force, the artificial neural network algorithm with 7.749% in the Y -axis force, and RSM with 0.93% in the surface roughness. Keywords Cutting force · Cutting parameters · Surface roughness · Response surface methodology · Ensemble machine learning · Artificial neural network Abbreviations RSM ANOVA MAPE ANN SVR DT K-NN Fx Fy Ra B Response surface methodology Analysis of variance Mean absolute percentage error Artificial neural network Support vector regression Decision tree K-nearest neighbor X-axis force (N) Y -axis force (N) Surface roughness (μm) Vc fz Ap HB MLP DF Adj SS Adj MS Cutting speed (m/min) Feed per tooth (mm/tooth) Depth of cut (mm) Brinell hardness Multilayer perceptron neural network Degree of freedom Adjusted sum of squares Adjusted mean squares 1 Introduction Murat Ozsoy [email protected] 1 Industrial Engineering Department, Faculty of Engineering, Sakarya University, Sakarya, Turkey 2 Mechanical Engineering Department, Faculty of Engineering, Sakarya University, Sakarya, Turkey Machinability can be defined as the ease with which the material is machined in terms of specific energy, specific horsepower, or shear stress. In general, the larger the shear stress or specific power values, the more difficult the material is to machine and form, requiring greater forces and lower 123 Arabian Journal for Science and Engineering speeds [1]. One of the criteria used to evaluate machinability is cutting force. Forces generated during milling operations are among the critical cost items. High force values during machining cause power and energy loss [2]. In addition, the roughness that appears on the surfaces because of high force values reduces the processing quality [3]. Parameters such as cutting speed, depth of cut, spindle speed, cutting tool, cooling type, etc., affect machinability [4]. High surface quality and low force values can be achieved by finding the optimum levels in the machining parameters; for this reason, the response surface method is frequently used [5]. Experimental, theoretical, and modeling studies using different values of processing parameters are summarized below. AISI 321 steel is stainless steel widely used in several industries. Therefore, researchers have conducted many studies on the machinability of this material. Siddiquee et al. studied AISI 321 austenitic stainless-steel material. They used the Taguchi method for experiment design and found that parameters that affect the surface roughness had been speed, cutting fluid, feed, and hole-depth [6]. In a different study, Vereschaka et al. [7] investigated metal cutting tools actions on AISI 321 materials. They determined that coating with thinner nanolayers performed better, particularly at high speeds. Pekşen and Kalyon studied the optimization of cutting parameters during the machining of AISI 430 material on a lathe. During the study, optimization was conducted using the surface roughness results [8]. In another study, Ross et al. studied the performance of coated carbide tools with cryogenic cooling in machining titanium alloy material with high strength and corrosion resistance. They investigated the optimum cutting parameters [9]. Li et al. studied a milling simulation work about surface quality and compared experimental results. They investigated the effects of parameters for AISI H13 steel [10]. Zhang et al. investigated optimum parameters in milling 300 M steel under different lubrication types. They advised cryogenic minimum quantity lubrication for low surface roughness and cutting force [11]. Choudhury et al. conducted experimental research on the end milling of bamboo composites via the Taguchi method. Spindle speed, feed, depth of cut, and milling cutter were chosen as cutting parameters. According to optimization analysis, the depth of cut had the maximum effect on the force, and the milling cutter was the dominant parameter on temperature [12]. Effects of fiber orientations and direction of machining on cutting forces and surface roughness in the milling of ceramic matrixed carbon fiber reinforced composites were investigated by Zhang et al. [13]. They reported that the machining parameters had essential importance. Çakıroğlu investigated the cutting force, and surface roughness of the Inconel 718 superalloy in the turning process in different environmental conditions. He used the Taguchi method to 123 design experiments and then optimized the results by GreyTaguchi Relational analysis [14]. Karabulut et al. studied the effects of machining variables on the milling force and tool wear during milling of Al7075 and the open cell SiC foam metal matrix composite using the Taguchi and the Response Surface Method. They found that cutting depth was the dominant parameter [15]. In another study, Badiger et al. produced Al and Ti multilayer coatings on WC tool insert with the chemical composition of TiN/AlN and examined the machinability of MDN431 alloyed steel. They developed quadratic mathematical models using regression analysis and artificial neural network [16]. In addition to previous studies, machine learning techniques for parameter optimization and estimating the results of experiments have recently become popular. Some of the studies are summarized below. Abbas et al. worked on the algorithm using an artificial neural network (ANN) with the Edgeworth-Pareto method to optimize the cutting parameter in CNC face milling operations. They aimed to reduce production costs and increase accuracy by optimizing surface roughness and minimum unit volume material removal rates [17]. Jurkovic et al. [18] compared several machine learning methods for predicting cutting parameters in turning operation. Machine learning methods used for prediction are support vector regression (SVR), polynomial regression, and the ANN. As a result, the SVR performed better than the ANN for cutting force and surface roughness estimation. In another study [19], CO2 hydrogenation optimization was performed using the ANN and the RSM. As a result, it is stated that the ANN provides satisfactory results in a noisy non-linear process. In the study by Daniel et al. [20] machining parameters of hybrid composites in Al5059/SiC/MoS2 milling were estimated. Taguchi S/N ratio analysis, ANN, and Gray relational analysis were performed. The ANN proved to be the most successful. Another study focused on predicting tool wear during the rotation of the Inconel 718. According to the average absolute percentage error (MAPE) results, the ANN was the most successful method [21]. Pimenov et al. used artificial intelligence methods to estimate the surface roughness, considering the main drive power and tool wear. They ensured the most efficient use of the cutting tool by estimating maximum tool wear, machining time, and cutting power to create a certain surface roughness [22]. Balasubramanian et al. analyzed the change of cutting forces applied to the tool according to the cutting parameters for end milling operation using a deep neural network. CutPro simulation software automatically changed and simulated the parameters. As a result, it was stated that the neural network formed by choosing the optimum parameters was found with an error of less than one percent of the estimation rates [23]. Correa et al. aimed to predict surface roughness in high-speed milling with bayesian networks. These network methods are used Arabian Journal for Science and Engineering for estimation. As a result, Bayesian networks were strong and successful, with 81.2% [24]. The study by Gupta aimed to predict tool power, surface roughness, and tool wear in turning operations. Artificial neural networks, support vector regression, and response surface methodology were used for the prediction model. The three methods were compared using data from twenty-seven experiments. As a result, it has been concluded that the artificial neural network and the support vector regression methods are good compared to the response surface methodology [25]. In the machining of AISI 1045 steel, parameters such as the feed per tooth, the cutting speed, the flank wear, the machined length, the sliding distance, the processing time were chosen by Pimenov et al. [26]. They improved the surface roughness and reduced the cutting power, thus reducing the machining cost and time by determining the optimum cutting conditions. Besides, they conducted a multilayer regression analysis. In the study of Natarajan et al. [27] the surface roughness of brass C26000 material was estimated. A prediction back propagation ANN model is designed. The designed model was compared with the experimental data, and it was concluded that there was no significant difference, and that ANN was found to be dependable. As mentioned in the literature survey above, there is limited numerical, analytical, or experimental research investigating the effect of cutting force and surface roughness for AISI 321 material on the milling process. Many studies investigating the cutting parameters during the milling of AISI 321 were found in current literature review However, none of the previous studies has not done extensive research on the optimization and prediction of both force and surface roughness. On the other hand, the ensemble application of DT, K-NN and ANN algorithms, which have not been used before, has been seen as successful for the results. It is thought that it will be useful to apply it for future state prediction in similar experiments. Therefore, this article aims to fill this gap, examine the force, and surface roughness during milling of AISI 321. One of the primary purposes of this study is to optimize the cutting parameters in a milling operation, and the other is the prediction of the experimental results. This exploratory study investigated how axial forces and surface quality affect the milling process and optimized cutting parameters by response surface methodology. While estimating the experimental results, a new perspective was presented by looking for an answer to the question, "Do the ensemble machine learning methods increase the prediction accuracy of machine learning methods?" which is the main hypothesis of the study. The paper is organized as follows: the materials and the methods used in the study are presented in Sect. 2. The results and discussions are given in Sect. 3. Prediction of the results of experiments with machine learning are given in Sect. 4. Finally, the study is concluded in Sect. 5. Fig. 1 The architectural structure of the study 2 Material and Methods The stages of the study consist of the following five steps. These are: 1. Experimentation: In this study, experiments were conducted for milling AISI material. 2. Determination of effects of parameters and the optimum parameter levels: The effects of the parameters on the results were determined by ANOVA and the optimum levels were found by the RSM. 3. Development and training of models: RSM, ANN, DT, K-NN, and ensemble machine learning methods were used to detect the experimental results. The dataset is divided into 80% training and 20% testing. 4. Evaluation of the results: The method with the most successful prediction level was decided by MAPE between the measured and predicted values of experiments. The architectural structure of the study is shown below in Fig. 1. First, a solid model of the part used in the experimental study was created. Then, using the solid model, the G-codes created for performing the experiments on the CNC milling 123 Arabian Journal for Science and Engineering Fig. 2 Technical representation and CAM model of the workpiece Table 1 The chemical content of the workpiece [28] Element Cr Ni C Mn P S Si Ti N % 17–19 9–12 0.08 2 0.045 0.03 0.75 0.5–0.7 0.1 machine. Experiments were carried out according to the input parameters shown in Table 5. F x and F y forces generated during machining have been obtained, and surface roughness was measured. After this step, the study was divided into two parts. The effects of parameters on outputs were investigated in the first part using the ANOVA method. Then, RSM was used to find the optimum parameter and level values. In the second part, to train machine learning methods, experiments were divided into two datasets as training and testing. Initially, machine learning methods were applied independently. Then, ensemble methods were used to improve the prediction performance. RSM, individual machine learning algorithms, and ensemble machine learning algorithms were compared to check whether the targeted prediction success rates were achieved. Appropriate prediction methods were selected for the parameters. Table 2 Mechanical properties for the workpiece [28] 2.1 Work Piece Material Choosing suitable cutting tool material and geometry is vital for achieving low surface roughness and low axial forces. Therefore, during the experiments, an aluminum titanium nitride coated cutting tool with a diameter of 10 mm, 40° helix angle, 0.5 mm corner radius, 4-flute, 22 mm cutting depth, 70 mm long, which is suitable for end milling, was used. The geometry of the cutting tool is given in Fig. 3, and the cutting tool properties are presented in Table 3. Three different parameters, such as cutting speed, depth of cut, and feed per tooth, were chosen at three levels. Selected parameters and levels are specified in Table 4. The workpiece material was AISI 321 with approximately 150 × 50 × 8 mm3 . The technical representation and CAM model of the workpiece are given in Fig. 2. AISI321 stainless steel is like 304 quality stainless material in terms of its structure. It has excellent resistance to corrosion with a maximum of 0.7% titanium additive. Welding capability is extremely high, but machinability is low. It is widely used in the food and machinery industries, especially in parts operating at high temperatures (Aircraft exhaust manifolds, blowers, heat exchangers, et al.). Milling is widely used in the manufacture of parts from this material. Since the machinability of this material is low, it is cost-effective to examine tool wear and optimize cutting parameters during milling. Table 1 shows the chemical, and Table 2 shows the mechanical properties of the AISI 321 material. 123 Yield strength Ultimate tensile strength Elongation Hardness 205 MPa 515 MPa 40% 217 HB Fig. 3 Cutting tool geometry 2.2 Sample Preparation and Cutting Parameters 2.3 Force and Surface Roughness Measurement All experimental studies were performed in Hartford brand four axes CNC vertical machining center. The G codes used in the end milling process were created using the 2d trajectory Arabian Journal for Science and Engineering Table 3 Cutting tool properties Brand Kyocera Description 4QFRM100-220-10-R05-VE Tool material Solid carbide Workpiece material Stainless steel/Cast iron/Steel Diameter (D) 10 mm Number of flutes 4 Cutting length (Lc) 22 mm Total length (L) 70 mm Corner radius (r) 0.5 mm Helix angle (Ha) 40° Coating AlTiN Table 4 Parameters and levels Fig. 4 Schematic diagram of the test setup Cutting speed (m/min) Symbol Levels Cutting speed (m/min) Vc 60 70 Depth of cut (mm) Ap 0.25 0.5 Feed per tooth (mm/tooth) fz 0.04 0.05 milling strategy in the PTC Creo Parametric software. There are twenty-seven experiments in the study. Each sample contains nine experiments. A total of three samples were used for twenty-seven experiments. Each experiment was repeated three times. After three repetitions, the mathematical average of the maximum forces obtained in the X and Y axes was taken. The X axis is parallel to the machining direction, and the Y axis is perpendicular. The coordinate system used in the study can be seen in Fig. 2. The workpiece used in the experiments was fixed to the 3-component Kistler 9257B dynamometer with two screws. It has a maximum capacity of five KN measurement range on each axis. Kistler 5010 charge amplifier, data acquisition interface DT9837B and Spinscope software were used for data acquisition of cutting force during end milling operations. The schematic view of the experimental setup can be seen in Fig. 4. The forces in the X and Y axes were examined during this study. One thousand samples per second were collected during cutting force measurement. Each experiment was repeated three times. After repeated experiments, the data were exported to Microsoft Excel software. A data set was created for each experiment by averaging the data of three measurements. Maximum values for F x and F y were determined from the generated datasets. Also, HOMMEL Tester T 500 Mobile semi-automatic device was used for surface roughness measurement. Measurements were made from three regions, the beginning, middle and end of the machined surface, and the average was taken. 2.4 Machine Learning and Statistical Methods Machine learning and statistical methods were used to develop prediction models. Among the statistical methods, RSM was preferred. Machine learning methods were applied in two stages. First, the three basic machine learning methods are discussed separately. These methods are ANN, DT, and K-NN. Then, these four algorithms are combined to increase the prediction accuracy. Vote ensemble method, one of the ensemble machine learning methods, was used for merging. Analysis of variance was used to determine the effects of parameters on the results. For parameter dependent outcome estimation, RSM-based regression was performed. In addition, optimization based on the desirability function was made via RSM. Error rates of prediction models compared to MAPE values. The methods are described in detail in Sects. 3 and 4. 3 Results and Discussions 3.1 Experimental Plan and Results The experimental plan and results are given in Table 5. The experiments were planned according to the 33 factorial design. So, 27 experiments were conducted. Axial forces the F x and the F y were measured while the experiments were taking place. Maximum force values were used in the analyses. The average surface roughness measurements were made on test specimens after the experiments. 123 Arabian Journal for Science and Engineering Table 5 Experimental plan and results Exp. No Input parameters Vc (m/min) Fz (mm/tooth) Calculated values Ap (mm) n (rpm) Vf (mm/min) Results Time (s) F x (N) F y (N) Roughness (Ra) 1 60 0.04 0.25 1910 306 10.78 24 42 0.42 2 60 0.04 0.5 1910 306 10.78 85 112 0.47 3 60 0.04 0.75 1910 306 10.78 117 165 0.53 4 60 0.05 0.25 1910 382 8.64 55 70 0.44 5 60 0.05 0.5 1910 382 8.64 115 148 0.52 6 60 0.05 0.75 1910 382 8.64 143 205 0.58 7 60 0.06 0.25 1910 458 7.21 70 90 0.55 8 60 0.06 0.5 1910 458 7.21 124 177 0.61 9 60 0.06 0.75 1910 458 7.21 155 235 0.68 10 70 0.04 0.25 2228 356 9.27 32 45 0.48 11 70 0.04 0.5 2228 356 9.27 87 111 0.55 12 70 0.04 0.75 2228 356 9.27 139 176 0.65 13 70 0.05 0.25 2228 445 7.42 38 54 0.53 14 70 0.05 0.5 2228 445 7.42 100 129 0.58 15 70 0.05 0.75 2228 445 7.42 150 194 0.7 16 70 0.06 0.25 2228 534 6.18 38 59 0.6 17 70 0.06 0.5 2228 534 6.18 97 132 0.62 18 70 0.06 0.75 2228 534 6.18 160 205 0.64 19 80 0.04 0.25 2546 407 8.11 35 43 0.59 20 80 0.04 0.5 2546 407 8.11 77 88 0.62 21 80 0.04 0.75 2546 407 8.11 117 140 0.67 22 80 0.05 0.25 2546 509 6.48 35 47 0.63 23 80 0.05 0.5 2546 509 6.48 84 100 0.66 24 80 0.05 0.75 2546 509 6.48 114 163 0.71 25 80 0.06 0.25 2546 611 5.40 38 46 0.62 26 80 0.06 0.5 2546 611 5.40 80 120 0.68 27 80 0.06 0.75 2546 611 5.40 137 187 0.72 3.2 ANOVA Results The ANOVA table is used to express numerically the effect of the parameters with various statistical values. Quality characteristics vary by changing quality parameters. The sum of the squares of the quality attributes is calculated as the difference between the mean value and the results of each experiment. Each design parameter affects this total. The result remaining from the total of these effects indicates the error. By dividing the sum of squares of the parameters by the sum of squares, the contribution of that parameter as a percentage is found. The mean squares are calculated by dividing the sum of squares for each design parameter and error by the degrees of freedom. As the F value of the parameter increases, its effect on the result also increases. If the P value is below 0.05, the parameter is significant [29]. With the help of ANOVA, the effects of cutting speed, feed per 123 tooth, and depth of cut on cutting force and surface roughness were found. Table 6 shows the ANOVA results for the cutting force in the X-direction. In the variance analysis performed in this study, the confidence interval was 95%, and the significance level was 5%. The effects of parameters in ANOVA were calculated by comparing the F-Value of each parameter. The contribution of each factor to the total variation is shown in the last column of the tables. Table 6 shows the ANOVA results for the F x . The contribution rates of the parameters on cutting force in the X-direction were 3.617% for Vc, 4.129% for fz, and 87.495% for Ap, respectively. From these results, the effective parameter on the cutting force in the X direction was the depth of cut with 87.495%. Table 7 shows the analysis of variance results for the F y . The contribution rates of the parameters on cutting force in the Y direction were 5.905% for Vc, 6.672% for fz, and Arabian Journal for Science and Engineering Table 6 ANOVA results for F x Table 7 ANOVA results for F y Source DF Adj SS Vc 2 1734.3 fz 2 1980.1 Ap 2 41,949.4 Vc × fz 4 1074.1 Adj MS 867.1 990 20,974.7 F-value 47.49 P-value Contribution% 0 3.617 54.22 0 4.129 1148.72 0 87.495 2.24 268.5 14.71 0.001 12.2 0.002 1.857 0.144 0.353 Vc × Ap 4 890.8 222.7 fz × Ap 4 169.7 42.4 Error 8 146.1 18.3 Total 26 47,944.5 Source DF Adj SS Vc 2 5357.9 2678.9 fz 2 6054.3 3027.1 Ap 2 76,656.5 38,328.3 Vc × fz 4 1403.7 350.9 Vc × Ap 4 540.8 135.2 7.16 fz × Ap 4 564.4 141.1 7.48 0.008 0.622 Error 8 Total 26 151 90,728.5 84.489% for Ap, respectively. From these results, the effective parameter on the cutting force in the Y direction was the depth of cut with 86.489%. Table 8 shows the analysis of variance results for Ra. The contribution rates of the parameters on surface roughness were 38.485% for Vc, 17.417% for fz, and 33.244% for Ap, respectively. From these results, the most influential parameter on the surface roughness was the cutting speed with 38.485%. Since there is not much difference between the levels of fz parameter, its effect is less compared to other parameters. 3.3 Effects of Parameters Contour plots can show relationships with the parameters in two dimensions. The F x , F y , and Ra variations obtained from experiments are given in Figs. 5, 6, and 7. The plot gives the values of the Z variable for the combinations of the X and Y variables. The X and Y values are located along the X and Y axes, while the contour lines and stripes represent the Z value. In the contour drawings, it is seen that the values from dark red to light red tend to increase, and the values from light blue to dark blue reach the highest values. 2.32 0.304 100 Adj MS 18.9 F-value P-value Contribution% 141.96 0 5.905 160.42 0 6.672 2031.13 0 84.489 0 1.547 0.009 0.596 18.6 0.166 100 Figure 5 shows the contour plots of F x . Force distribution according to fz and Vc in 5a, force distribution according to Ap–fz in 5b, and force distribution according to Ap–Vc in 5c are given. Figure 6 shows the contour plots of F y . Force distribution according to fz and Vc in 6a, force distribution according to Ap–fz in 6b, and force distribution according to Ap–Vc in 6c are given. As the Ap and fz levels increased, the force values increased. It is seen that the increase in Vc also tends to increase the force. A maximum value of around 160 N is seen for F x . For F y , a maximum value of around 190 N is observed. Figure 7 shows the contour plots of Ra. Surface roughness distribution according to fz and Vc in 7a, force distribution according to Ap–fz in 7b, and force distribution according to Ap–Vc in 7c are given. It is seen that the surface roughness is higher at the maximum levels of all parameters. Values of about 0.7 and above were found. From contour plots (Figs. 5a, 6a) cutting speed and feed per tooth had minor effects on cutting forces results. As the depth of cut increases (Figs. 5b, c and 6b, c), the cutting forces in the X and Y axes also increase in direct proportion. Higher depth of cut values generates more force. This increases the roughness due to a greater deformation of the chip being pushed more violently against the machined surface. As a result, the surface quality decreases [30]. These results overlap with the ANOVA results. It is observed (Fig. 7a–c) that the surface roughness value increased with increasing parameter levels. 123 Arabian Journal for Science and Engineering Table 8 ANOVA results for Ra Source Vc DF 2 Adj SS Adj MS F-Value P-Value Contribution% 0.067222 0.033611 51.93 0 38.485 fz 2 0.030422 0.015211 23.5 0 17.417 Ap 2 0.058067 0.029033 44.86 0 33.244 Vcxfz 4 0.010356 0.002589 4 0.045 5.928 VcxAp 4 0.001911 0.000478 0.74 0.592 1.094 fzxAp 4 0.001511 0.000378 0.58 0.684 Error 8 0.005178 0.000647 Total 26 0.174667 Fig. 5 Effect of parameters on F x a F x versus fz, Vc b F x versus Ap, fz c F x versus Ap, Vc (calculated with Minitab software) Fig. 6 Effect of parameters on F y a F y versus fz, Vc b F y versus Ap, fz c F y versus Ap, Vc (calculated with Minitab software) Fig. 7 Effect of parameters on Ra a Ra versus fz, Vc b Ra versus Ap, fz c Ra versus Ap, Vc (calculated with Minitab software) 123 0.865 2.964 100 Arabian Journal for Science and Engineering 3.4 Probability Analysis Figure 8 shows normal probability plots of residual values and prediction values for surface roughness and force. Deviation from a straight line represents a departure from normality. Looking at the figure, half of the data is on the right and the other half on the left. It is seen that the data follow a straight line, and the proposed model is compatible [31]. The distribution of the measured and calculated results was checked. The probability graph confirmed the values given in Table 5 in Fig. 8. The probability plot of the F x is given in Fig. 8a, that of the F y in 8b, and that of the Ra in 7c. Graphs are drawn at 95% confidence intervals. As seen in the graphs, the test results are quite close to the central axis. Therefore, these data can be used for optimization and experimental research. i=1 βi X i + k i=1 − 69454 f zx f z − 111, 3x Apx Ap − 92.5V cx f z R = 94.13 2 (2) F y = − 988 + 16.92x V c + 17525x f z + 307x Ap − 0.0725x V cx V c − 62983x f zx f z − 157.4x V cx f z − 2.33x V cx Ap + 22.57x f zx Ap R 2 = 96.96 (3) Ra = − 0.974 + 0.01783x V c + 20.53x f z + 0.237x Ap − 0.235x f z R = 82.36 RSM can optimize multiple parameters simultaneously. It also determines the linear, square and interaction effect of the parameters. Estimation of a quality characteristic with high reliability is achieved by multiple regression. RSM model consisting of at least three factors should be designed for each control parameter. The relationship between the control parameter and the quality characteristic is obtained by RSM [31]. This study used experimental data to improve the mathematical models using RSM in milling by MINITAB 19. The relationship between input parameters in RSM problems and their responses is usually expressed through a quadratic polynomial equation given below Eq. (1). k F x = − 510 + 3.75x V c + 14375x f z + 308.3x Ap 2 3.5 Regression by RSM Y = β0 + to Eq. 1, and a stepwise method was used. Equations (2), (3) and (4) indicate regression equations for F x , F y and Ra, respectively. βii X i2 + k k βi j X i X j + ε i=1 j=1 (1) Equation 1 is a coded model for second-order polynomial equation. In this equation, Y is the corresponding response, X i and X j are process parameters, β 0 is a constant, β ii and β ij are the first and the second-degree coded input parameters and parameters interactions of linear, quadratic and second order terms. k is the number of independent parameters, and the ε is the error term. k is 3 in this work. β i is the regression coefficient, and β 0 is the average response in an experimental design. The term regression coefficient of β ij represents the interaction between the process parameters X i and X j . Mathematical models were derived between responses and milling parameters using experimental results according (4) The models were checked by employing the coefficient of determination R2 . The value of R2 is always desired bigger. All the R2 values are over 80% in this work, which shows the high correlation between the experimental results and predicted values. 3.6 Optimization by RSM The desirability function method, one of the most popular techniques, was used to find optimum levels of parameters. With this method, a desirability value di is calculated for each response, which measures how close the optimum value of the factors is to the desired value. These values are then used to generate composite desirability for the response variable. d i ranges from 0 to 1 for any given response. In this study, it is desired to have minimum force and surface roughness values [32]. The measured quality characteristics of the predicted response are transformed to a dimensionless desirability value (d i ) by this function. The d i value increases when the desirability of the sharp response rises. This study aimed to reduce force in milling and have minimum surface roughness, so the more minor (the better-quality characteristic) was chosen. The equation is given in Eq. (5). w 1 U − yi di = 0 U −T yi < T T ≤ yi ≤ U yi > U (5) Here T is the target value of the ith response yi , T is the acceptable lower limit, U is the allowable upper limit for 123 Arabian Journal for Science and Engineering Fig. 8 a Probability plot of F x b Probability plot of F y c Probability plot of Ra (calculated with Minitab software) 4 Prediction of the Results of Experiments with Machine Learning 4.1 Development of Prediction Models The study used artificial neural networks, decision trees, k-nearest neighbor algorithms from basic individual algorithms, and vote methods from ensemble algorithms to develop prediction models. It is aimed to predict new experimental results. The parameters of the algorithms were determined heuristic through experience, trial, and error. Rapidminer Studio Version 9.8 program was used to determine the success of the models. 4.2 Artificial Neural Network Fig. 9 Response optimization plot for parameters (calculated with Minitab software) Artificial neural networks are an essential classification tool that includes parallel computing programs that work like the human brain. Based on the precedent examples and their relationships, the computer systems that make learning decisions are peculiar to humans. Artificial neural networks consist of artificial neurons whose function is presented in Eq. (6) [34]. y= f this response [33]. The optimum levels were obtained from the analysis, results shown in Fig. 9 by using Minitab 19 software. Figure 9 shows optimum cutting conditions and optimized response parameters. The high and low represent the boundary conditions for the parameters. Optimum values are in red. Where y indicates the optimum value obtained, d indicates desirability for each input. It is aimed to minimize surface roughness and force values with optimized parameter levels. The desirability value was obtained at 0.968. According to research, optimum levels are 60.80 m/min for cutting speed, 0.040 mm/tooth for feed per tooth, and 0.250 mm for depth of cut. The optimized values are 0.419 for the Ra, 49.183 for the F y , and 31.524 for the F x . 123 d wi xi (6) i Here d is the total number of inputs, w is the weights, and x is the inputs. Multilayer perceptron neural network (MLP), the most used artificial neural network model, consists of three layers: input, hidden, and output. Layers are connected by process elements that enable information transmission. The number of process elements in the input and output layer is determined according to the problem. The number of elements in the hidden layer is defined by trial and error to achieve the best performance. The weights that show the importance of the information are chosen randomly at the beginning [35]. Arabian Journal for Science and Engineering similarity between two samples is needed to find the location of the nearest neighbors. These can be expressed as the Euclidean, Manhattan, and Minkowski Distance [38, 39]. 4.5 Ensemble Machine Learning Fig. 10 Artificial neural network architecture [35] In the study, feed-forward back propagation MLP is used. The neural network consists of three inputs, one hidden layer containing three neurons, and one output, as seen in Fig. 10. Artificial neural network models are set up separately for each cutting parameter (F x , F y , Ra). The inputs consist of experimental parameters. The parameters used for the neural network are shown in Table 10. It was used as a sigmoid, popular in studies as an activation function [36]. 4.3 Decision Tree The Decision Tree algorithm has a tree structure consisting of root, intermediate, and leaf nodes. The model is easy to understand and interpret. It can work with continuous and categorical data, even with missing or missing data. Because of these features, it is one of the most widely used algorithms. Some criteria are used to determine which variable the root node will be. These are information gain, gini index, and gain ratio. The choice of this criterion affects the success of the algorithm. The working steps of the algorithm start from the root node, then continue by dividing up to the intermediate, and then the leaf node [37]. 4.4 K-Nearest Neighbor The nearest neighbor algorithm classifies unlabeled samples by assigning them to the class of k most similar labeled samples. The user determines the k number here. Since the decision is made by voting, the odd number k should be preferred. The number k should be greater than one, but it should be considered that a vast number will reduce the method’s effectiveness. Apart from this, a formula that measures the It is thought that using ensemble methods by combining them instead of using machine learning algorithms alone will increase prediction accuracy [40]. The prediction ability of ensemble methods is often stronger than using basic algorithms individually. Ensemble algorithms are divided into dependent and independent according to how they are connected. According to the algorithm type, it is classified as homogeneous and heterogeneous [41]. Four ensemble algorithms are bagging, boosting, stacking, and voting. Bagging is independent and homogeneous, boosting is dependent and homogeneous, stacking is dependent and heterogeneous, and voting is independent and heterogeneous. In this study, three heterogeneous machine learning algorithms were used in parallel, so the voting method was used. 5 Comparisons of the Results In the study, five models were established for each result (F x , F y , Ra) using RSM, neural network, DT, K-NN, and Vote (neural network + DT + K − NN) methods. It is aimed to estimate the result values to be obtained according to the cutting parameters in the models. The parameters of the algorithms used in the models were determined heuristically, working performances of the models were compared. Performances are evaluated according to the MAPE value is presented in Eq. (7). n 100 Yi − Ŷ MAPE : Yi n (7) i=1 Here, Y i is the measurement value, Ŷ is the predictive value. If the MAPE value of the models is below 10%, they are considered as ’very good’, between 10 and 20% as ’good’, between 20 and 50% as ’acceptable’, and above 50% as ’wrong’ [42]. The predicted results were compared with the experimental results on the five selected samples. According to these comparisons, the most suitable method was selected for the experimental set used in the study. In all model’s, the learning rate is 0.01, momentum 0.9, and sigmoid function were used in the neural network, mixed measure and mixed Euclidian were used in K-NN, and since the target value of the data set is not nominal, the DT criterion is chosen as at least square. Apart from these values, the selected parameter for the individual values is shown in Table 9. Null values are used for parameters other than these. 123 Arabian Journal for Science and Engineering Table 9 Parameter of individual machine learning algorithms Neural Network DT K-NN Parameters Fx Neural.Net_Cycle 200 Maximal Depth 10 k 11 Fy 750 30 9 Ra 200 10 3 Results Algorithms In the study, individual algorithms were combined with the voting method from the ensemble machine learning algorithms. Moreover, in ensemble algorithms, the same parameters are used when the algorithms are used individually. To measure F x , F y and Ra values, the regression models derived from Vc, fz and Ap was estimated with RSM, individual and ensemble machine learning algorithms. Measured values of experiments and prediction values of models are shown in Table 10. According to Table 10, MAPE values of the models, which express the error rate, are shown in Fig. 11. Low error rates are desirable for the success of the model. When the MAPE values are examined; it is evaluated as ’good’ for the F x and ’very good’ for the F y and the Ra according to the Fig. 11. The lowest error for the F x result was obtained when the vote method was used with a MAPE value of 11.163%. The second method with an error rate is the RSM method with 12.834%. In the model established with the DT algorithm, the MAPE value is 17.298%. Furthermore, an error rate of 18.195% was seen in the model set with ANN. The highest error occurred when the K-NN algorithm was used with 30.568%. The lowest error for the F y ’s result was obtained with 7.749% when using ann. In the model established with the Vote method, it is seen that the MAPE value is the second with 10.586%. In the model based with RSM, there was an error of 19.41% and a DT with an error rate of 26.056%. The Table 10 Measured values of experiments and prediction values of models Method RMS ANN DT K-NN Vote Cutting parameters Result in F x Measured Result in F y Result in Ra Vc fz Ap Prediction Measured Prediction Measured Prediction 80 0.05 0.5 80 0.05 0.75 84 91.44 100 97.52 0.66 0.65 114 133.73 163 155.88 0.71 0.71 80 0.06 0.25 38 28.58 46 24.85 0.62 0.61 80 0.06 0.5 80 84.79 120 88.85 0.68 0.67 80 0.06 0.75 137 127.08 187 152.86 0.72 0.73 80 0.05 0.5 84 106.3 100 106.3 0.66 0.67 80 0.05 0.75 114 168.18 163 168.18 0.71 0.69 80 0.06 0.25 38 55.39 46 55.39 0.62 0.66 80 0.06 0.5 80 125.5 120 125.5 0.68 0.69 80 0.06 0.75 137 194.98 187 194.98 0.72 0.7 80 0.05 0.5 84 98.5 100 130.5 0.66 0.61 80 0.05 0.75 114 146.5 163 199.5 0.71 0.67 80 0.06 0.25 38 37 46 74.5 0.62 0.61 80 0.06 0.5 80 98.5 120 130.5 0.68 0.61 80 0.06 0.75 137 157.5 187 199.5 0.72 0.67 80 0.05 0.5 84 81.55 100 101.84 0.66 0.64 80 0.05 0.75 114 92.6 163 121.58 0.71 0.65 80 0.06 0.25 38 73.69 46 81.58 0.62 0.61 80 0.06 0.5 80 83.87 120 103.45 0.68 0.65 80 0.06 0.75 137 92.6 187 123.7 0.72 0.65 80 0.05 0.5 84 83.71 100 107.41 0.66 0.64 80 0.05 0.75 114 118.57 163 157.47 0.71 0.67 80 0.06 0.25 38 50.43 46 57.86 0.62 0.63 80 0.06 0.5 80 86.6 120 113.86 0.68 0.65 80 0.06 0.75 137 126.02 187 166 0.72 0.68 123 Arabian Journal for Science and Engineering Fig. 11 Comparison of MAPE of models highest error occurred when the K-NN algorithm was used with 30.568%. When the result of the Ra is examined, it is seen that the RSM has the lowest error rate, that is, the most successful algorithm. The algorithm with the highest error rate was the DT algorithm with 6.38%. 6 Conclusions This paper optimized the cutting parameters on cutting forces and surface roughness in trajectory milling of the AISI 321 material in wet conditions. Optimal cutting parameters were determined by the RSM method and the desirability function. In addition, a new perspective was presented by estimating the experimental results with ensemble methods. There are three output results in the study: F x , F y , and Ra. The aim of the study is to predict the experimental results in the most accurate way. Both machine learning and statistical methods were used for prediction. The statistically based method is the RSM. In machine learning methods, first, three basic machine learning methods were discussed individually. These methods are ANN, DT, and K-NN. Then, aiming to increase the prediction accuracy, these four algorithms were combined with the vote ensemble method. The easiest way to combine different algorithms is by voting. Therefore, it is preferred. In addition, the aggregation method was used in the vote method. Since the target value of the experimental set is continuously variable, the models are regression based. Performance evaluations of models vary according to the analysis method used in the model. Since regression-based models were developed in the study, their performance was evaluated according to the error value. Models were compared according to their MAPE values, as it is the most frequently used measurement value when examining error values. The lowest MAPE values for the models provide the most successful accuracy rates. The results from this study are summarized below. When the results are examined, it can be said that the prediction accuracies of the models show that a different algorithm is successful for each experimental result. If the F x is to be estimated, the prediction model should be developed with the vote ensemble method. The error rate was obtained as 11.163%. If the F y is to be estimated, the prediction model should be developed with the ANN algorithm. The error rate was 7.749%. If the Ra is to be predicted, the estimation model should be developed with the RSM method. The error rate was 0.930%. When the MAPE values are examined; it is evaluated as ’good’ for the F x and ’very good’ for the F y and the Ra. The main hypothesis of the study is: “The ensemble machine learning methods are machine learning methods that increase their prediction accuracy". The results of the vote ensemble method show that it is validated for the F x output. Performing the experiments requires long time and high cost. The number of experiments needed can be significantly reduced as future situations will be predicted by the developed prediction models. The ensemble application of DT, K-NN, and ANN algorithms, which have not been used before, has been seen as successful for the F x result. It is thought that it will be useful to apply it for future state prediction in similar experiments. ANOVA results showed that while the effective parameter on the cutting forces both in X and Y direction was the depth of cut, the cutting speed had been the most dominant parameter on the surface roughness. The contribution rates of the parameters on cutting force in the X-direction were 3.617% for the Vc, 4.129% for the fz, and 87.495% for Ap, respectively. From these results, the effective parameter on the cutting force in the X direction was the depth of cut with 87.495%. The contribution rates of the parameters on cutting force in the Y direction were 5.905% for the Vc, 6.672% for the fz, and 84.489% for Ap, respectively. From these results, the effective parameter on the cutting force in the Y direction was the depth of cut with 86.489%. The contribution rates of the parameters on surface roughness were 38.485% for the Vc, 17.417% for the fz, and 33.244% for the Ap, respectively. From these results, the most influential parameter on the surface roughness was the cutting speed with 38.485%. As a result of response surface optimization and desirability function method, optimum milling levels of parameters are 60.80 m/min for the cutting speed, 0.040 mm/tooth for the feed per tooth, and 0.250 mm for the depth of cut. The effects of parameters on the force and the surface roughness were supported by contour plots. 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