Microsoft Word - ETASR_V13_N3_pp10659-10663 Engineering, Technology & Applied Science Research Vol. 13, No. 3, 2023, 10659-10663 10659 www.etasr.com Danh & Cuong: Surface Roughness Modeling of Hard Turning 080A67 Steel Surface Roughness Modeling of Hard Turning 080A67 Steel Bui Thanh Danh Faculty of Mechanical Engineering, University of Transport and Communications, Vietnam danhdaiduong@utc.edu.vn Nguyen Van Cuong Faculty of Mechanical Engineering, University of Transport and Communications, Vietnam nguyencuong@utc.edu.vn (corresponding author) Received: 17 February 2023 | Revised: 15 March 2023 | Accepted: 17 March 2023 Licensed under a CC-BY 4.0 license | Copyright (c) by the authors | DOI: https://doi.org/10.48084/etasr.5790 ABSTRACT Surface roughness is an important parameter to evaluate the quality of a machining process in mechanical manufacturing. The construction of a surface roughness model of a machining process is the basis for predicting surface roughness corresponding to each certain case. This paper presents the construction of a surface roughness model in 080A67 steel turning. An experimental process was carried out with a total of 15 experiments, designed according to the Box-Behnken matrix. The cutting speed, feed rate, and cutting depth were changed in each experiment, and surface roughness values were measured to build a model that showed the mathematical relationship between surface roughness and the three cutting parameters. A second surface roughness model was also constructed using the Box-Cox transformation. The accuracy of these two models was compared through five coefficients: R 2 , R 2 (pred), R 2 (adj), Percentage Absolute Error (PAE), and Percentage Square Error (PSE). The results showed that all these coefficients of the model using the Box-Cox transformation were better than those of the first one. In detail, the values of R 2 , R 2 (pred), R 2 (Adj), PAE, and PSE of the first model were 94.55%, 12.79%, 84.74%, 8.79%, and 1.42%, while for the second model were 99.09%, 85.42%, 97.44%, 2.26%, and 0.18%, respectively, showing that the accuracy of the surface roughness model was improved by using the Box-Cox transformation. Keywords-hard turning; 080A67 steel; surface roughness; Box-Cox transformation I. INTRODUCTION Steel of the 080A67 type is manufactured using the UK standard and is equivalent to some steel types from other countries, such as 65G steel in Bulgaria and Poland, 66Mn4, Ck67 in Germany, 65Mn in China, 1066, 1566, and G15660 in the USA [1]. This type of steel has the advantage of high wear resistance and is used to manufacture parts that require wear resistance in the cement industry, thermoelectricity, sliding plates, etc. [2]. Some studies were carried out to evaluate the characteristics of this steel type such as evaluating the degree of deformation when hot rolling [3], and evaluating friction coefficient [4]. Many studies have been carried out to improve the advantages of this type of steel, such as improving wear resistance by the heat treatment method [5-8], improving compressive residual stress in magnetic processing [9], developing technical solutions to produce high-quality products from the casting process [10], investigation of solutions to reduce microcracking on the surface [11], studies on the solutions to increase the hardness of the surface [12-13], etc. This type of steel is increasingly used to manufacture parts with high-quality requirements, which usually need some finished faces to assemble with other parts. Therefore, ensuring that the surfaces used for assembling have small roughness is often a requirement when machining this type of steel. However, the number of published studies on surface roughness and, in particular, on the machining process of this type of steel is quite small. The surface roughness with flat grinding was studied in [14], the surface roughness and the productivity of the machining when grinding the outer round was investigated in [15], the change of hardness of the surface layer when grinding was studied in [16-19], the cutting force when milling was evaluated in [20], and the surface hardening phenomenon when spark machining was studied in [21]. The turning method, and the hard turning method in particular, are increasingly used to machine products with high accuracy requirements [22-24]. So, this study aims to cover the lack of published studies on the hard turning of 080A67. While several different criteria can be used to evaluate a turning process, surface roughness is the most frequently used parameter [25-26]. The reason behind this is possibly that surface roughness has a direct influence on wear resistance, fatigue strength, and chemical corrosion resistance of the product surface [27]. In addition, measuring the surface roughness in an experimental process is easier than measuring other cutting parameters such as cutting force, cutting heat, etc. Engineering, Technology & Applied Science Research Vol. 13, No. 3, 2023, 10659-10663 10660 www.etasr.com Danh & Cuong: Surface Roughness Modeling of Hard Turning 080A67 Steel [28]. A commonly used method to study surface roughness in the turning process is the construction of a model to predict it under certain conditions. However, as the accuracy of the predicted surface roughness results relies on the accuracy of the model, it is necessary to improve it. So, this study also aims to improve the accuracy of the surface roughness model. II. EXPERIMENTAL PROCESS AND RESULTS ANALYSIS This study used 080A67 steel in the experimental process. The steel samples had a length and diameter of 300 and 30mm, respectively. The steel workpieces were heat treated through two steps of quenching and tempering. When quenching, the steel workpieces were heated to 830°C and then cooled in an oil medium. When tempering, the steel workpieces were heated to 540°C and then cooled in an oil medium. A Metrology VHT-A0950D instrument was used to test the hardness of the steel workpieces. All the steel workpieces had a similar hardness, at around 52HRC. Table I shows the percentages by mass of the main chemical elements in steel, which were analyzed using a GNR S3 Mililab 300 emission spectrometer. TABLE I. CHEMICAL ELEMENTS OF 080A67 STEEL Element C Si Mn P S Cr Ni % 0.67 0.24 1.02 0.002 0.002 0.24 0.22 A Doosan Lynx 220L lathe was used for the experiments. A TiN-coated Kyocera TNMG160404GP was used as a cutting tool in the experimental process. This cutting piece is commonly used in the hard-turning process [29]. The cutting piece parameters, provided by the manufacturer, were: 12⁰ front angle, 6.5° back angle, and 0.4mm tip radius. Straight oils were used in the experimental process, mixed with water to a concentration of 4%, and brought into the cutting zone with a flow rate of 8lt/min, and 2.6atm pressure, according to the oil manufacturer. Surface roughness was measured by an SJ301 gauge. To reduce the influence of random errors on the precision of the experimental process, each experiment was carried out with 3 steel samples, and the surface roughness was measured on each steel sample at least 3 times in succession. So, the surface roughness value in each experiment was the average of at least 9 measurements. The experimental matrix was designed according to the Box-Behnken form, which is the most commonly used type of matrix to construct the relationship between input and output parameters [30]. The values of cutting speed, feed rate, and cutting depth were altered in each experiment. These parameters can be quickly adjusted by the machine operator [31-32]. Three values were chosen for each cutting parameter, corresponding to the encoding levels -1, 0, and 1. Table II shows the parameter values chosen for each level. Table III shows the experiment matrix for the fifteen experiments, built according to the Box-Behnken method. TABLE II. VALUES OF CUTTING PARAMETERS AT LEVELS Parameter Unit Code symbol Actual symbol Value at levels –1 0 1 Cutting speed m/min x1 vc 140 180 220 Feed rate mm/tooth x2 fz 0.25 0.45 0.65 Depth of cut mm x3 ap 0.3 0.4 0.5 The experimental process was carried out according to the sequence of the experiments, as shown in Table III. The surface roughness of each steel sample was measured at least 3 times, and the average value of the measurements was taken. The average surface roughness of the 3 steel samples is denoted as Ra1, Ra2, and Ra3, respectively. Table III summarizes the mean of the surface roughness in each experiment. TABLE III. EXPERIMENT MATRIX AND RESULTS Exp. Code value Actual value Response x1 x2 x3 v (m/min) fd (mm/rev) ap (mm) Ra1 (m) Ra2 (m) Ra3 (m) Ra (m) 1 -1 -1 0 140 0.25 0.4 0.728 0.801 0.865 0.798 2 1 -1 0 220 0.25 0.4 1.055 1.026 1.210 1.097 3 -1 1 0 140 0.65 0.4 0.922 0.966 1.010 0.966 4 1 1 0 220 0.65 0.4 1.547 1.602 1.513 1.554 5 -1 0 -1 140 0.45 0.3 1.392 1.422 1.386 1.400 6 1 0 -1 220 0.45 0.3 2.224 2.432 2.331 2.329 7 -1 0 1 140 0.45 0.5 0.886 0.853 0.874 0.871 8 1 0 1 220 0.45 0.5 1.378 1.378 1.378 1.378 9 0 -1 -1 180 0.25 0.3 1.101 1.082 1.108 1.097 10 0 1 -1 180 0.65 0.3 1.623 1.499 1.387 1.503 11 0 -1 1 180 0.25 0.5 0.801 0.703 0.860 0.788 12 0 1 1 180 0.65 0.5 1.171 1.182 1.160 1.171 13 0 0 0 180 0.45 0.4 0.882 0.884 0.883 0.883 14 0 0 0 180 0.45 0.4 0.879 0.901 0.875 0.885 15 0 0 0 180 0.45 0.4 0.886 0.892 0.883 0.887 The Minitab v.16 software was used to analyze the experimental data in Table III. The surface roughness model was constructed according to (1). The commonly used coefficients to evaluate the accuracy of a regression model, such as the surface roughness model, are R2, R2(pred) and R 2(adj). The closer these coefficients are to 1, the higher the accuracy of the regression model [30]. �� = 0.8850 + 0.2903 ∙ � + 0.1767 ∙ � − 0.2651 ∙ � + 0.2867 ∙ �� − 0.0680 ∙ �� + 0.3227 ∙ �� − 0.0722 ∙ � ∙ �− 0.1055 ∙ � ∙ � − 0.0057 ∙ � ∙ � (1) Equation (1) had R2, R2(pred) and R2(adj) of 94.55%, 12.79%, and 84.74%, respectively. Thus, although R2 has a quite large value, the other coefficients have quite small values, Engineering, Technology & Applied Science Research Vol. 13, No. 3, 2023, 10659-10663 10661 www.etasr.com Danh & Cuong: Surface Roughness Modeling of Hard Turning 080A67 Steel especially the coefficient R2(pred). This means that if (1) is used to predict the surface roughness, the prediction results will be much different from the experiment results [30]. Therefore, the accuracy of the regression model to predict surface roughness should be increased. III. IMPROVING THE ACCURACY OF THE SURFACE ROUGHNESS MODEL Two commonly used methods to increase the accuracy of regression models are converting data according to Box-Cox and Johnson [33, 34]. In this study, the Box-Cox transformation was used to improve the precision of the surface roughness model, as it was also used in several studies, such as the 65G steel surface grinding [14], SCM435 steel centerless grinding [33], 3X13 steel milling [34], and EN 353 steel milling [35]. The condition to perform the Box-Cox transformation was that the surface roughness values in the experiment were not normally distributed [30]. Therefore, it is necessary to check the distribution rules of the surface roughness values when testing. Figure 1 shows a distribution chart of surface roughness values. Fig. 1. The distribution rule of surface roughness values. In Figure 1, the red dots represent the surface roughness values and the blue lines represent the normal distribution. It can be seen that the red dots lie far away from the center line and there are red dots outside the limits of the normal distribution. This proves that the set of surface roughness values was not distributed according to the normal rule. On the other hand, the probability value P-value was 0.021, which is lower than the significance level (the significance level is usually chosen as 0.05). This also confirms that the set of surface roughness values was not distributed according to the normal rule [31], meaning that the set of surface roughness data was eligible to perform the Box-Cox transformation. Figure 2 shows the Box-Cox transformation graph. It can be noted that the converted coefficient lambda () equals -1.00, which means that the relationship between the surface roughness before and after the transformation is represented by [30]: ����� . � = ��� �� = ��� (2) where Ra and Ra(Box.) are the values of surface roughness before and after the Box-Cox transformation, respectively. Table IV shows the surface roughness values before and after the Box-Cox transformation. Fig. 2. Box-Cox transformation model of surface roughness TABLE IV. SURFACE ROUGHNESS VALUES BEFORE AND AFTER BOX-COX TRANSFORMATION Exp. Ra(m) Ra(Box.) (dimensionless) 1 0.798 1.253 2 1.097 0.912 3 0.966 1.035 4 1.554 0.644 5 1.400 0.714 6 2.329 0.429 7 0.871 1.148 8 1.378 0.726 9 1.097 0.912 10 1.503 0.665 11 0.788 1.269 12 1.171 0.854 13 0.883 1.133 14 0.885 1.130 15 0.887 1.127 Fig. 3. Distribution rule of surface roughness data after the Box-Cox transformation. Figure 3 shows the distributions of the surface roughness values after the Box-Cox transformation. It can be noted that all the red dots lie inside the limits of the distribution rule. The probability value P-value was 0.348, which was a lot larger than the significance level. This also confirms that these data were distributed according to the normal rule. Engineering, Technology & Applied Science Research Vol. 13, No. 3, 2023, 10659-10663 10662 www.etasr.com Danh & Cuong: Surface Roughness Modeling of Hard Turning 080A67 Steel The following equation can be constructed from the surface roughness dataset after the Box-Cox transformation: �� ��� . � = 1.1299 − 0.1800 ∙ � − 0.1434 ∙ � + 0.1595 ∙ � − 0.1698 ∙ �� + 0.0007 ∙ �� − 0.2057 ∙ �� − 0.0125 ∙ � ∙ � − 0.0343 ∙ � ∙ � − 0.0422 ∙ � ∙ � (3) Combining (2) and (3) gives the following surface roughness model: �� = ������ .� (4) where �� ��� . � is given by (3). Equation (4) has R2, R2(pred) and R2(adj) coefficients of 99.09%, 85.42%, and 97.44%, respectively. These values are very close to 1, proving that (4) can be used to predict surface roughness with high accuracy. The two models were used to predict surface roughness. Note that the model given by (1) is the one without data transformation, and the model given by (4) is the one after the Box-Cox transformation. The value of surface roughness when predicted using (1) is denoted Ra (1), and the surface roughness value predicted using (4) is denoted as Ra (2). Table V shows the results of surface roughness when testing and predicting according to these two models. TABLE V. SURFACE ROUGHNESS VALUES WHEN TESTING AND PREDICTING ACCORDING TO 2 MODELS Exp. Ra (measured) Ra (1) (1) Ra (2) (4) 1 0.798 0.565 0.786 2 1.097 1.290 1.068 3 0.966 1.062 0.990 4 1.554 1.499 1.600 5 1.400 1.364 1.350 6 2.329 2.155 2.226 7 0.871 1.045 0.886 8 1.378 1.414 1.429 9 1.097 1.222 1.154 10 1.503 1.587 1.506 11 0.788 0.704 0.787 12 1.171 1.046 1.113 13 0.883 0.885 0.885 14 0.885 0.885 0.885 15 0.887 0.885 0.885 PAE 8.79% 2.26% PSE 1.42% 0.18% The PAE and PSE parameters were used to evaluate the accuracy of the two models, and the smaller their values, the higher the accuracy of the model. PAE and PSE were calculated according to [31]: !"# = �$ % ���&'�()*'+�,���-*'+./0'+� ���&'�()*'+� % ∗ 100 (5) !2# = �$ 3���45�67859� − ���:859;<=59�> � ∗ 100 (6) where N is the number of experiments (N=15). Equations (5) and (6) were used to calculate PAE and PSE according to the data in Table V, and Table VI presents the results. The R2, R2(pred), and R2(Adj) of the two models given by (1) and (4) are summarized in this table. TABLE VI. PARAMETERS OF THE SURFACE ROUGHNESS MODELS Model R 2 R 2 (pred) R 2 (Adj) PAE PSE Without transformation (1) 94.55% 12.79% 84.74% 8.79% 1.42% Using Box-Cox transformation (4) 99.09% 85.42% 97.44%. 2.26% 0.18% According to the data in Table VI, the coefficients R2, R 2(pred), and R2(Adj) of the model using the Box-Cox transformation (4) were higher than those of the model without data transformation (1). On the other hand, both PAE and PSE of the model using the Box-Cox transformation were smaller than those of the model without data transformation. This shows that the model with the Box-Cox transformation had a higher accuracy than the other model. IV. CONCLUSION The construction of a regression model representing the relationship between input and output data is a method usually used in experimental studies in general and in the field of machine building in particular. 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