# Surface Feature Prediction Modeling and Parameter Optimization for Turning TC17 Titanium Alloy

Authors: Zhibo Deng; Zhe Wang; Xuehong Shen
Journal: International Transactions on Electrical Energy Systems
 (2022)

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## Abstract

Surface integrity has a very significant effect on surface roughness and surface microhardness. These are the main characteristics of surface integrity. The present study investigated the influence of the cutting depth (ap), the cutting speed (vc), and the feed rate (f) on the surface roughness (Ra) and surface microhardness (HV) in turning TC17 titanium alloy. Data obtained from the Box-Behnken design experiments were used to develop the response surface methodology (RSM) and artificial neural network (ANN) models. Through analysis of variance (ANOVA), the relative effects of each cutting parameter on the responses have been determined. To examine the interaction effects of cutting parameters, 3D surface plots were generated. The desirability function approach (DFA) was used to optimize cutting parameters to achieve the lowest surface roughness and highest surface microhardness. The results show that ANN response prediction models have higher prediction accuracy and lower error than RSM prediction models. The optimization parameters are 60 m/min cutting speed, 0.06 mm/r feed rate, and 0.2 mm cutting depth for the minimum surface roughness and maximum surface microhardness with a maximum error of 2.83%.


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## Body

## 1. Introduction

Titanium alloy materials have lots of advantages of high strength, good toughness, and high adaptability to forging temperature and are widely used in the manufacture of aerospace parts [1]. However, in the titanium alloy cutting process, the heat and force actions are prone to drastic changes, and the chips are very easy to adhere for causing significant tool wear [2, 3], which makes it difficult to control the concerning characteristics. It is indispensable to study the surface roughness and microhardness of titanium alloy cutting. Many professionals have conducted a large number of research on the cutting of titanium alloy materials. Mersni et al. [4] analyzed the influence of cutting speed, depth of cut, and feed per tooth on the three-dimensional surface roughness using Taguchi’s method and optimized the best cutting parameters to obtain the best machining workpiece’s surface. Kumar et al. [5] employed multiresponse grey relational analysis (GRA) technology to optimize process parameters and observed the influence of cutting parameters on the surface roughness and material removal rate through the main effect diagram. Kiswanto et al. [6] used a cemented carbide tool with a diameter of 1 mm to conduct a milling experiment by changing the spindle speed and feed rate in high-speed cutting under the condition of a fixed cutting depth to measure the surface roughness under different variable combinations. They discovered that a slower cutting speed and feed rate are better for improving surface processing quality. Thirumalai et al. [7] established the quadratic regression empirical prediction model of surface roughness and cutting temperature of turning titanium alloy. Applying signal-to-noise ratio (SNR), the proportion of cutting speed on surface roughness is 38%, and the feed rate is 25%. The most important factor affecting cutting temperature is cutting speed, and the least influential factor is cutting depth. Samin et al. [8] employed Taguchi’s experimental design method to carry out Ti6Al4V turning experiments. The analysis showed that the feed rate and the cutting depth are the most relevant parameters that affect surface roughness and cutting force. Through the turning experiments with different tool radius, Mazid et al. [9] obtained the optimized parameter range of surface roughness from 0.5 μm to 1 μm based on a cutting speed of 60–250 m/min, the feed speed 0.1 mm/r and the cutting depth 0.5 mm. Matras et al. [10] put forward that the influence of cutting speed on surface roughness can be ignored, and it takes the minimum surface roughness as the objective to optimize the process parameters. Seung et al. [11] analyzed the impact of machining tools on the machinability of titanium alloy. The consequences show that the dynamic range of cutting force and surface roughness of coated cemented carbide tool and cermet tool is larger than cemented carbide tool, and the influencing factors of tool life are tool material, cutting speed, and feed. By studying the influence of tool microstructure on chip morphology, cutting force, surface state, and surface roughness, Qian et al. [12] analyzed and summarized the test data and found that the key factor to improve the machinability of TC21 titanium alloy was the microstructure. Besides, scholars pay attention to the tool wear because the material is easy to stick to the tool in the process of titanium alloy. Aramcharoen [13] found that low-temperature cooling can reduce friction between the tool and the chip, improve production efficiency and tool life, and create a thinner secondary deformation zone. Taking 0.1 mm as the tool wear limit, Priarone et al. [14] proposed that low-temperature cooling can extend the tool life of uncoated cemented carbide tools by 2 minutes, CBN tools about 7.2 minutes, and PCD tools with different grain sizes by 14 minutes compared with traditional oil cooling and low-temperature cooling. With the emergence of new processing methods, Che-Haron [15] carried out the cutting experiments of Ti-6Al-2Sn-4Zr-6Mo with different grain sizes (1.0 μm and 0.68 μm) uncoated cemented carbide tools to describe that the main forms of tool wear are excessive cutting. Furthermore, it is stated that the finer the grain size, the longer is the tool life. Muhammad et al. [16] used unified Ti6Al4V turning experiments to analyze tool wear and energy distributions to evaluate the tool wear rate and energy generated by different cutting conditions. Due to the large contact length and high chip compression ratio, serious tool wear and a large energy zone appear in high-speed cutting.At present, the research on titanium alloy mainly focuses on Ti6Al4V. Compared with others, the TC17 has bigger yield strength, smaller elongation, and lower elasticity modulus. The research on TC17 titanium alloy is still relatively very lacking. Therefore, it is necessary to study the surface roughness and surface microhardness of turning TC17. The results can conduct the selection of cutting parameters according to the application requirements.


## 2. Experimental Conditions and Methods

The experimental material is titanium alloy TC17, which is anα + β dual-phase alloy rich in α phase. Its chemical composition is depicted in Table 1, and its fundamental material properties are presented in Table 2 [17, 18]. The experimental piece is Φ60 mm × 280 mm bar material. The tool model is a hard alloy tool YG6, with a rake angle of 6°, and a relief angle of 10°. In order to reduce the cutting temperature, a large amount of cutting fluid with a cooling effect should be poured into the cutting area. Because the thermal conductivity of titanium alloy is low, which is only 1/7 of steel and 1/6 of aluminum, the heat can’t be quickly transferred with the chips in the machining process. When turning and cutting titanium alloys, emulsions or water-soluble cutting fluids with extreme pressure additives are often used, which is not easy to reach the ignition temperature. It is better not to use gaseous coolant in titanium alloy processing, so as to avoid toxic substances and hydrogen embrittlement and also prevent high-temperature stress corrosion cracking of titanium alloy. In this experiment, the emulsion is selected for cooling According to the actual processing conditions. To reduce the interference of other nonconcerned factors on the reliability of the experimental results, each set of experiments adopts a new blade. Using the Box-Behnken design experimental program [19], which is shown in Table 3, to plan the experiment with cutting speed, feed, and cutting depth as experimental factors with three levels defined for each factor.Table 1
Chemical composition of TC17.
ElementWt. (%)ElementWt. (%)Al5.23Fe0.3Sn1.97C0.05Zr1.9N0.05Mo4.06H0.01Cr4.04O0.12TiBalanceTable 2
Material properties of TC17.
Material propertiesValueElastic modulus112 (GPa)Tensile strength1960 (MPa)Yield strength1890 (MPa)Density4.55 (g/cm3)Hardness41 (HRC)Elastic modulus112 (GPa)Tensile strength1960 (MPa)Table 3
Chosen parameters and levels.
CodeExperimental factorsUnitsLevels123ACutting speedm/min306090BFeed ratemm/r0.060.120.18CCutting depthmm0.10.20.3The length of processing for each set of parameters is 10 millimeters. Figure1 illustrates the experimental conditions. The experimental results are surface roughness (Ra) and surface microhardness (HV), which were measured using the conventional surface roughness tester TR240 and the digital display Micro Vickers hardness tester HV-50, respectively. To reduce measurement error, the average of three measurements is applied to each result. Table 4 represents the precise experimental arrangement and measurement data.Figure 1
The experimental conditions.Table 4
The response surface experimental results.
No.Cutting speedvc (m/min)Feed ratef (mm/r)Cutting depthap (mm)Surface roughnessRa(μm)Surface microhardness HV1600.120.21.364552300.060.30.794353600.120.21.284604900.060.10.74385300.060.10.684406900.180.32.514497600.180.22.174508600.060.20.744569900.180.11.8141210600.120.11.3544011600.120.21.3245812600.120.21.244913900.060.30.8342114300.120.21.5842615900.120.21.3742016300.180.32.3248017600.120.21.4545218600.120.31.5346819600.120.21.2144820300.180.12.27426


## 3. Prediction Model and Influence Law

### 3.1. Analysis of Variance (ANOVA)

Analysis of variance (ANOVA) is one method for assessing the significance of input factors on response variables. In addition, it is a convenient and swift solution process that is widely accepted and utilized. Table5 are the results of ANOVA for surface roughness (Ra). In Table 5, the P-Value does not exceed 0.05, which indicates that the influence of the input parameters is established, and the cutting parameters play a key role in surface roughness. The A, B, and C input parameters expend percentages for surface roughness (Ra) are 0.31%, 91.67%, and 2.38% respectively. It indicates that B has the principal influence on the surface roughness (Ra), shortly followed by C. The P-Value of A to surface roughness (Ra) is greater than 0.05, indicating that it can be ignored.Table 5
Analysis of variance forRa.
SourceDFAdj SSAdj MSF-valueP-valueC. (%)SignifModel95.740.6445.52<0.000197.62YESA10.0180.0181.260.2880.31B15.395.39384.57<0.000191.67C10.140.149.770.01082.38AB10.0140.0140.970.34750.24AC10.0560.0564.010.07320.95BC10.0330.0332.320.15860.56A210.0140.0141.010.3380.24B217.38E-037.38E-030.530.48450.13C213.73E-033.73E-030.270.61720.06Error100.140.014Total195.88For the surface microhardness (HV), the ANOVA results are shown in Table 6. Through analysis, the percentage contributions of process parameters for A, B, and C were defined as (7.90%, 1.28%, and 16.56%), respectively. It shows that C with 16.56% contributions occupies the first position in influencing surface microhardness (HV). The next factor is A with 7.90% contributions. For the low contribution of B (1.28%), it shows that B has no significant influence on the surface microhardness (HV).Table 6
Analysis of variance forHV.
SourceDFAdj SSAdj MSF-valueP-valueC. (%)SignifModel95300.78588.9815.51<0.000193.31YESA1448.9448.911.820.00647.90B172.972.91.920.1961.28C1940.9940.924.780.000616.56AB1105.12105.122.770.12711.85AC1105.12105.122.770.12711.85BC11596.131596.1342.03<0.000128.10A211750.141750.1446.08<0.000130.81B2162.6462.641.650.2281.10C2191.6491.642.410.15141.61Error10Total19


### 3.2. Response Surface Method(RSM) Modeling Development

#### 3.2.1. Regression Analysis

Regression analysis is based on a large number of test data analysis results, using mathematical methods to establish the relationship model between input variables and output variables. It can be used to predict the value of the variable and is widely used in industrial production and science research. The response surface method (RSM) is a test method that considers interference factors and is accepted by the public [20, 21]. The regression model obtained through experimental design can be expressed as in the following Equation:(1)y=β0+∑i=1mβixi+∑i=1mβiixi2+∑i<jmβijxixj,where, β0 is the constant term, βi is the linear effect of xi, βii is the second-order effect of xi, βij is the interactive effect between xi and xj, and xi andxj are the input and response variables, respectively.Equations (2) and (3) can be used to calculate prediction models for surface roughness (Ra) and surface microhardness (HV) (3).(2)Ra=0.792−0.01vc+8.02f−3.25ap−0.02vcf+0.02vcap+10.06fap+0.00007vc2+14.39f2+3.68ap2R2=0.9762,(3)HV=408.86+3.62vc−623.18f−343.90ap−2.01vcf−1.21vcap+2354.16fap−0.02vc2+1325.75f2+577.27ap2R2=0.9331.The correlation coefficientsR2 of the regression equations that advanced for the predictive surface roughness and surface microhardness were computed as R2=98% and R2=93%, respectively. Figure 2 depicts a comparison of experimental results and predicted values obtained from regression equations. Most of the true values are scattered on the predicted value, and a small part of the true values are scattered on both sides of the predicted value, indicating that the model fits well with the actual results. As a result, the regression model can estimate the surface feature, including Ra and HV.Figure 2
Comparison of prediction models forRa and HV.


#### 3.2.2. Surface Plot in 3D

Figure3 shows the variation of Ra with the interaction of machining process factors. The cutting depth in Figure 3(a) is 0.2 mm. The surface roughness increases linearly as the feed rate (f) increases from 0.06 mm/r to 0.18 mm/r. The effect of cutting speed on the Ra is less than the feed rate. The roughness is at its worst state level when the feed rate and cutting speed are both set to low levels.Figure 3
The influence of the machining factor onRa. (a) Interaction of f and vc on Ra, (b) interaction of ap and vc on Ra, and (c) interaction of ap and f on Ra.
(a)(b)(c)The interaction of cutting speed and cutting depth onRa is illustrated in Figure 3(b). In this analysis, the feed rate is selected by 0.12 mm/r, and the fluctuation range of Ra is from 1.2 to 1.6 μm. It has been discovered that both the cutting depth and the cutting speed have some very slight effects on the Ra. The Ra response surface graph of the cutting depth and feed rate at a cutting speed of 60 m/min is shown in Figure 3(c). In contrast, Ra is susceptible to feed rate fluctuations and less susceptible to cutting depth. The Ra reaches the maximum value of 2.4 μm with the machining parameter factor cutting speed which is 60 m/min, the feed rate is 0.18 mm/r, and the cutting depth is 0.3 mm.The 3D plot of milling parameters on surface microhardness (HV) was presented in Figure 4. In Figure 4(a), while the feed goes up from the initial value of 0.06 mm/r to 0.18 mm/r, the maximum surface microhardness is obtained at vc = 70 m/min. Figure 4(b) demonstrates that the surface microhardness rises with increasing cutting depth. Figure 4(c) demonstrates that the cutting depth continuously increases from 0.1 to 0.3 mm, while the microhardness decreases. The maximum microhardness value can be obtained under the condition of large feed and large cutting depth, up to nearly 490 HV. It can be seen from the interaction depicted and contour diagram of the comprehensive response surface that microhardness is sensitive to feed rate and cutting depth, which is consistent with the coefficient reflection of the established model.Figure 4
The influence of cutting parameters onHV. (a) The influence of f and vc on HV. (b) The influence of ap and vc on HV. (c) The influence of ap and f on HV.
(a)(b)(c)


## 3.1. Analysis of Variance (ANOVA)

Analysis of variance (ANOVA) is one method for assessing the significance of input factors on response variables. In addition, it is a convenient and swift solution process that is widely accepted and utilized. Table5 are the results of ANOVA for surface roughness (Ra). In Table 5, the P-Value does not exceed 0.05, which indicates that the influence of the input parameters is established, and the cutting parameters play a key role in surface roughness. The A, B, and C input parameters expend percentages for surface roughness (Ra) are 0.31%, 91.67%, and 2.38% respectively. It indicates that B has the principal influence on the surface roughness (Ra), shortly followed by C. The P-Value of A to surface roughness (Ra) is greater than 0.05, indicating that it can be ignored.Table 5
Analysis of variance forRa.
SourceDFAdj SSAdj MSF-valueP-valueC. (%)SignifModel95.740.6445.52<0.000197.62YESA10.0180.0181.260.2880.31B15.395.39384.57<0.000191.67C10.140.149.770.01082.38AB10.0140.0140.970.34750.24AC10.0560.0564.010.07320.95BC10.0330.0332.320.15860.56A210.0140.0141.010.3380.24B217.38E-037.38E-030.530.48450.13C213.73E-033.73E-030.270.61720.06Error100.140.014Total195.88For the surface microhardness (HV), the ANOVA results are shown in Table 6. Through analysis, the percentage contributions of process parameters for A, B, and C were defined as (7.90%, 1.28%, and 16.56%), respectively. It shows that C with 16.56% contributions occupies the first position in influencing surface microhardness (HV). The next factor is A with 7.90% contributions. For the low contribution of B (1.28%), it shows that B has no significant influence on the surface microhardness (HV).Table 6
Analysis of variance forHV.
SourceDFAdj SSAdj MSF-valueP-valueC. (%)SignifModel95300.78588.9815.51<0.000193.31YESA1448.9448.911.820.00647.90B172.972.91.920.1961.28C1940.9940.924.780.000616.56AB1105.12105.122.770.12711.85AC1105.12105.122.770.12711.85BC11596.131596.1342.03<0.000128.10A211750.141750.1446.08<0.000130.81B2162.6462.641.650.2281.10C2191.6491.642.410.15141.61Error10Total19


## 3.2. Response Surface Method(RSM) Modeling Development

### 3.2.1. Regression Analysis

Regression analysis is based on a large number of test data analysis results, using mathematical methods to establish the relationship model between input variables and output variables. It can be used to predict the value of the variable and is widely used in industrial production and science research. The response surface method (RSM) is a test method that considers interference factors and is accepted by the public [20, 21]. The regression model obtained through experimental design can be expressed as in the following Equation:(1)y=β0+∑i=1mβixi+∑i=1mβiixi2+∑i<jmβijxixj,where, β0 is the constant term, βi is the linear effect of xi, βii is the second-order effect of xi, βij is the interactive effect between xi and xj, and xi andxj are the input and response variables, respectively.Equations (2) and (3) can be used to calculate prediction models for surface roughness (Ra) and surface microhardness (HV) (3).(2)Ra=0.792−0.01vc+8.02f−3.25ap−0.02vcf+0.02vcap+10.06fap+0.00007vc2+14.39f2+3.68ap2R2=0.9762,(3)HV=408.86+3.62vc−623.18f−343.90ap−2.01vcf−1.21vcap+2354.16fap−0.02vc2+1325.75f2+577.27ap2R2=0.9331.The correlation coefficientsR2 of the regression equations that advanced for the predictive surface roughness and surface microhardness were computed as R2=98% and R2=93%, respectively. Figure 2 depicts a comparison of experimental results and predicted values obtained from regression equations. Most of the true values are scattered on the predicted value, and a small part of the true values are scattered on both sides of the predicted value, indicating that the model fits well with the actual results. As a result, the regression model can estimate the surface feature, including Ra and HV.Figure 2
Comparison of prediction models forRa and HV.


### 3.2.2. Surface Plot in 3D

Figure3 shows the variation of Ra with the interaction of machining process factors. The cutting depth in Figure 3(a) is 0.2 mm. The surface roughness increases linearly as the feed rate (f) increases from 0.06 mm/r to 0.18 mm/r. The effect of cutting speed on the Ra is less than the feed rate. The roughness is at its worst state level when the feed rate and cutting speed are both set to low levels.Figure 3
The influence of the machining factor onRa. (a) Interaction of f and vc on Ra, (b) interaction of ap and vc on Ra, and (c) interaction of ap and f on Ra.
(a)(b)(c)The interaction of cutting speed and cutting depth onRa is illustrated in Figure 3(b). In this analysis, the feed rate is selected by 0.12 mm/r, and the fluctuation range of Ra is from 1.2 to 1.6 μm. It has been discovered that both the cutting depth and the cutting speed have some very slight effects on the Ra. The Ra response surface graph of the cutting depth and feed rate at a cutting speed of 60 m/min is shown in Figure 3(c). In contrast, Ra is susceptible to feed rate fluctuations and less susceptible to cutting depth. The Ra reaches the maximum value of 2.4 μm with the machining parameter factor cutting speed which is 60 m/min, the feed rate is 0.18 mm/r, and the cutting depth is 0.3 mm.The 3D plot of milling parameters on surface microhardness (HV) was presented in Figure 4. In Figure 4(a), while the feed goes up from the initial value of 0.06 mm/r to 0.18 mm/r, the maximum surface microhardness is obtained at vc = 70 m/min. Figure 4(b) demonstrates that the surface microhardness rises with increasing cutting depth. Figure 4(c) demonstrates that the cutting depth continuously increases from 0.1 to 0.3 mm, while the microhardness decreases. The maximum microhardness value can be obtained under the condition of large feed and large cutting depth, up to nearly 490 HV. It can be seen from the interaction depicted and contour diagram of the comprehensive response surface that microhardness is sensitive to feed rate and cutting depth, which is consistent with the coefficient reflection of the established model.Figure 4
The influence of cutting parameters onHV. (a) The influence of f and vc on HV. (b) The influence of ap and vc on HV. (c) The influence of ap and f on HV.
(a)(b)(c)


## 3.2.1. Regression Analysis

Regression analysis is based on a large number of test data analysis results, using mathematical methods to establish the relationship model between input variables and output variables. It can be used to predict the value of the variable and is widely used in industrial production and science research. The response surface method (RSM) is a test method that considers interference factors and is accepted by the public [20, 21]. The regression model obtained through experimental design can be expressed as in the following Equation:(1)y=β0+∑i=1mβixi+∑i=1mβiixi2+∑i<jmβijxixj,where, β0 is the constant term, βi is the linear effect of xi, βii is the second-order effect of xi, βij is the interactive effect between xi and xj, and xi andxj are the input and response variables, respectively.Equations (2) and (3) can be used to calculate prediction models for surface roughness (Ra) and surface microhardness (HV) (3).(2)Ra=0.792−0.01vc+8.02f−3.25ap−0.02vcf+0.02vcap+10.06fap+0.00007vc2+14.39f2+3.68ap2R2=0.9762,(3)HV=408.86+3.62vc−623.18f−343.90ap−2.01vcf−1.21vcap+2354.16fap−0.02vc2+1325.75f2+577.27ap2R2=0.9331.The correlation coefficientsR2 of the regression equations that advanced for the predictive surface roughness and surface microhardness were computed as R2=98% and R2=93%, respectively. Figure 2 depicts a comparison of experimental results and predicted values obtained from regression equations. Most of the true values are scattered on the predicted value, and a small part of the true values are scattered on both sides of the predicted value, indicating that the model fits well with the actual results. As a result, the regression model can estimate the surface feature, including Ra and HV.Figure 2
Comparison of prediction models forRa and HV.


## 3.2.2. Surface Plot in 3D

Figure3 shows the variation of Ra with the interaction of machining process factors. The cutting depth in Figure 3(a) is 0.2 mm. The surface roughness increases linearly as the feed rate (f) increases from 0.06 mm/r to 0.18 mm/r. The effect of cutting speed on the Ra is less than the feed rate. The roughness is at its worst state level when the feed rate and cutting speed are both set to low levels.Figure 3
The influence of the machining factor onRa. (a) Interaction of f and vc on Ra, (b) interaction of ap and vc on Ra, and (c) interaction of ap and f on Ra.
(a)(b)(c)The interaction of cutting speed and cutting depth onRa is illustrated in Figure 3(b). In this analysis, the feed rate is selected by 0.12 mm/r, and the fluctuation range of Ra is from 1.2 to 1.6 μm. It has been discovered that both the cutting depth and the cutting speed have some very slight effects on the Ra. The Ra response surface graph of the cutting depth and feed rate at a cutting speed of 60 m/min is shown in Figure 3(c). In contrast, Ra is susceptible to feed rate fluctuations and less susceptible to cutting depth. The Ra reaches the maximum value of 2.4 μm with the machining parameter factor cutting speed which is 60 m/min, the feed rate is 0.18 mm/r, and the cutting depth is 0.3 mm.The 3D plot of milling parameters on surface microhardness (HV) was presented in Figure 4. In Figure 4(a), while the feed goes up from the initial value of 0.06 mm/r to 0.18 mm/r, the maximum surface microhardness is obtained at vc = 70 m/min. Figure 4(b) demonstrates that the surface microhardness rises with increasing cutting depth. Figure 4(c) demonstrates that the cutting depth continuously increases from 0.1 to 0.3 mm, while the microhardness decreases. The maximum microhardness value can be obtained under the condition of large feed and large cutting depth, up to nearly 490 HV. It can be seen from the interaction depicted and contour diagram of the comprehensive response surface that microhardness is sensitive to feed rate and cutting depth, which is consistent with the coefficient reflection of the established model.Figure 4
The influence of cutting parameters onHV. (a) The influence of f and vc on HV. (b) The influence of ap and vc on HV. (c) The influence of ap and f on HV.
(a)(b)(c)


## 4. Artificial Neural Network (ANN)

Compared with the regression analysis, the artificial neural network (ANN) does not need to specify the mathematical model in advance, which avoids the shortcomings of the curve fitting method and improves the prediction modeling accuracy. ANN is widely used in prediction, classification, and other research due to its self-learning and self-adaptive advantages in processing random data and nonlinear data. Maheshwera et al. [22] used regression analysis and artificial neural network models to predict the Ra of AISI 52100 steel during hard turning. The difference between the calculated values of the model and the experimental results is particularly small. Using the ANN, Abbas et al. [23] successfully predicted the surface roughness of AZ61 magnesium alloy final turning with an accuracy of 1.35%. For the drilling process, Kolesnyk et al. [24] selected ANN to research CFRP/Ti alloy material and analyzed the cutting heat generated in the drilling process and the surface quality of the workpiece after drilling. The results show that ANN can be used to identify the drilling parameter-hole quality relationship. Sangwan et al. [25] and Kumar and Chauhan [26] proposed a method combining ANN and genetic algorithm to optimize the turning machining factors. It can be seen from the above research works that using the ANN model to examine the nonlinear relationship between the virtual machining parameters and the machining performance is effective in predicting the actual machining process.The structure of the neural network can be defined as 3-H-1, which stands for three input parameters (cutting speed, feed rate, and cutting depth) with H number of hidden layer nodes and one response (surface roughness or surface microhardness). The excitation function of the neural network adopts the hyperbolic tangent function (TanH) [27], which transforms values to be between −1 and 1 and its expression is given in the following Equation:(4)TanH=e2x−1e2x+1.


### 4.1. Application of ANN to Model (Ra)

According to Table7, some ANN structures were tested. Figure 5 depicts the best network topology, which is 3-9-1 based on a smaller RMSE and a higher R2. It is made up of three input layer nodes, nine hidden layer nodes, and one output layer node with a linear transfer function.Table 7
Performance of ANN structure ofRa.
Inp_Hid_OupRoot mean square error (RMSE)Coefficient of determination (R2)3-5-10.05080.98713-6-10.08860.96073-7-10.08810.96113-8-10.05040.98733-9-10.01710.99993-10-10.08180.9665Figure 5
The optimal network structure forRa.The mathematical model for surface roughness (Ra) derived by the ANN approach is shown in the following Equation with R2=99.99%:(5)Ra=1.9478−0.4451∗H1+1.7919∗H2−1.5120∗H3+3.1112∗H4−0.4457∗H5+0.5689∗H6+0.7477∗H7+3.1521∗H8−0.47247∗H9, where, (6)H1=TanH3.4307+−6.5460∗ap+8.7363∗f+−0.04552∗Vc,H2=TanH1.4897+1.6920∗ap+−15.8407∗f+0.0022∗Vc,H3=TanH−3.6149+8.3069∗ap+6.0278∗f+0.01098∗Vc,H4=TanH−2.59039+7.2156∗ap+3.4107∗f+0.0076∗Vc,H5=TanH3.5705−2.3971∗ap+−15.6305∗f+−0.02977∗Vc,H6=TanH−2.8044+0.1261∗ap+7.1547∗f+0.0197∗Vc,H7=TanH−0.5712+−3.5080∗ap+10.1420∗f+0.01147∗Vc,H8=TanH1.7555+−2.8133∗ap+−5.9964∗f+−0.0103∗Vc,H9=TanH−3.9836−1.9689∗ap+20.2767∗f+0.03528∗Vc,


### 4.2. Application of ANN to Model (HV)

In the same way, the test results of the several ANN architectures ofHV are shown in Table 8. The architecture chosen is 3-10-1 (Figure 6) with the highest R2 and the lowest RMSE.Table 8
Performance of ANN structure of HV.
Inp_Hid_OupRMSER23-5-111.32700.63093-6-11030050.69473-7-12.35320.98403-8-110.26150.69703-9-12.38820.98353-10-11.63290.9923Figure 6
The optimal network structure forHV.The mathematical model obtained by the ANN method for the surface microhardness (HV) is expressed in the following Equation with R2=99.23%:(7)HV=425.8282+25.4849∗H1+1.8094∗H10+298.8565∗H2+41.14935∗H3−22.76606∗H4−122.02144∗H5−19.6225∗H6−158.3730∗H7−38.6868∗H8−136.0233∗H9,where,(8)H1=TanH3.3995−8.1659∗ap−3.0219∗f−0.0270∗Vc,H2=TanH−2.7765+5.2553∗ap+3.6597∗f+0.0102∗Vc,H3=TanH1.8557+3.7416∗ap−17.2210∗f−0.0135∗Vc,H4=TanH2.2312−11.05189∗ap−1.0593∗f−0.0057∗Vc,H5=TanH−3.4709+7.0627∗ap−3.4015∗f+0.02637∗Vc,H6=TanH−6.0225+8.4248∗ap+25.9316∗f+0.02868∗Vc,H7=TanH−3.2211+3.0372∗ap+7.5765∗f+0.01766∗Vc,H8=TanH5.2797−3.4336∗ap−24.5623∗f−0.02859∗Vc,H9=TanH0.17486+2.9591∗ap−1.5697∗f−0.0149∗Vc,H10=TanH−2.6185+1.1293∗ap+16.5582∗f+0.01407∗Vc.Table9 and Figures 7 and 8 are the comparison of experimental and estimated by RSM and ANN, and the absolute percentage error(△) is calculated using the following Equation [22]:(9)Δ=yexp−ypredyexp×100%.Table 9
Comparison of the measured and predicted value.
No.Surface roughness (Ra)Surface microhardness (HV)Ra (μm) expRSM predANN predError (%) (RSM)Error (%) (ANN)HV (%) expRSM predANN predError (%) (RSM)Error (%) (ANN)11.361.44831.34146.491.37455480.1878455.84145.540.1820.790.76930.79192.620.24435443.4931434.54981.950.1031.281.44831.341413.154.80460480.1878455.84144.390.9040.70.83620.728919.454.12438503.8056437.63415.020.0850.680.88420.682830.020.41440445.1016439.84751.160.0362.512.48432.65081.025.61449514.1188447.080414.500.4372.172.23721.94513.1010.37450487.6745461.88178.372.6480.740.76290.74443.100.60456482.2466455.33195.760.1591.812.11771.815117.000.28412473.7475410.657914.990.33101.351.42211.35975.340.72440476.2698454.1628.243.22111.321.44831.34149.721.62458480.1878455.84144.840.47121.21.44831.341420.6911.78449480.1878455.84146.951.52130.830.96130.834715.820.57421487.6771418.874515.840.50141.581.51131.58474.350.30426440.0838434.13043.311.91151.371.51131.381510.310.84420484.2918418.274515.310.41162.322.43632.32265.010.11480484.4068479.36560.920.13171.451.44831.34140.127.49452480.1878455.84146.240.85181.531.54801.43741.176.05468495.6513462.10115.911.26191.211.44831.341419.6910.86448480.1878455.84147.181.75202.272.30972.30471.751.53426429.5155425.7280.830.06Average9.503.487.360.85Figure 7
Experimental, RSM, and ANN predicted results forRa.Figure 8
Experimental, RSM, and ANN predicted results forHV.For RSM and ANN, the maximum test errors for surface roughness are about 30.02% and 11.78%, respectively. The mean absolute percentage error between RSM and experimental values can be seen as 9.50%, whereas the same value is only 3.48% with the ANN model. In surface microhardness, the same maximum test errors for RSM and ANN are revealed as 15.84% and 3.22%, respectively. The mean absolute percentage errors between experimental and estimated by RSM and ANN are found to be 7.36% and 0.85%. Actual values and anticipated values for ANN and RSM are shown in Figures7 and 8. Thus, it can be seen that ANN is closer to the test results than RSM, showing a better fitting effect.


## 4.1. Application of ANN to Model (Ra)

According to Table7, some ANN structures were tested. Figure 5 depicts the best network topology, which is 3-9-1 based on a smaller RMSE and a higher R2. It is made up of three input layer nodes, nine hidden layer nodes, and one output layer node with a linear transfer function.Table 7
Performance of ANN structure ofRa.
Inp_Hid_OupRoot mean square error (RMSE)Coefficient of determination (R2)3-5-10.05080.98713-6-10.08860.96073-7-10.08810.96113-8-10.05040.98733-9-10.01710.99993-10-10.08180.9665Figure 5
The optimal network structure forRa.The mathematical model for surface roughness (Ra) derived by the ANN approach is shown in the following Equation with R2=99.99%:(5)Ra=1.9478−0.4451∗H1+1.7919∗H2−1.5120∗H3+3.1112∗H4−0.4457∗H5+0.5689∗H6+0.7477∗H7+3.1521∗H8−0.47247∗H9, where, (6)H1=TanH3.4307+−6.5460∗ap+8.7363∗f+−0.04552∗Vc,H2=TanH1.4897+1.6920∗ap+−15.8407∗f+0.0022∗Vc,H3=TanH−3.6149+8.3069∗ap+6.0278∗f+0.01098∗Vc,H4=TanH−2.59039+7.2156∗ap+3.4107∗f+0.0076∗Vc,H5=TanH3.5705−2.3971∗ap+−15.6305∗f+−0.02977∗Vc,H6=TanH−2.8044+0.1261∗ap+7.1547∗f+0.0197∗Vc,H7=TanH−0.5712+−3.5080∗ap+10.1420∗f+0.01147∗Vc,H8=TanH1.7555+−2.8133∗ap+−5.9964∗f+−0.0103∗Vc,H9=TanH−3.9836−1.9689∗ap+20.2767∗f+0.03528∗Vc,


## 4.2. Application of ANN to Model (HV)

In the same way, the test results of the several ANN architectures ofHV are shown in Table 8. The architecture chosen is 3-10-1 (Figure 6) with the highest R2 and the lowest RMSE.Table 8
Performance of ANN structure of HV.
Inp_Hid_OupRMSER23-5-111.32700.63093-6-11030050.69473-7-12.35320.98403-8-110.26150.69703-9-12.38820.98353-10-11.63290.9923Figure 6
The optimal network structure forHV.The mathematical model obtained by the ANN method for the surface microhardness (HV) is expressed in the following Equation with R2=99.23%:(7)HV=425.8282+25.4849∗H1+1.8094∗H10+298.8565∗H2+41.14935∗H3−22.76606∗H4−122.02144∗H5−19.6225∗H6−158.3730∗H7−38.6868∗H8−136.0233∗H9,where,(8)H1=TanH3.3995−8.1659∗ap−3.0219∗f−0.0270∗Vc,H2=TanH−2.7765+5.2553∗ap+3.6597∗f+0.0102∗Vc,H3=TanH1.8557+3.7416∗ap−17.2210∗f−0.0135∗Vc,H4=TanH2.2312−11.05189∗ap−1.0593∗f−0.0057∗Vc,H5=TanH−3.4709+7.0627∗ap−3.4015∗f+0.02637∗Vc,H6=TanH−6.0225+8.4248∗ap+25.9316∗f+0.02868∗Vc,H7=TanH−3.2211+3.0372∗ap+7.5765∗f+0.01766∗Vc,H8=TanH5.2797−3.4336∗ap−24.5623∗f−0.02859∗Vc,H9=TanH0.17486+2.9591∗ap−1.5697∗f−0.0149∗Vc,H10=TanH−2.6185+1.1293∗ap+16.5582∗f+0.01407∗Vc.Table9 and Figures 7 and 8 are the comparison of experimental and estimated by RSM and ANN, and the absolute percentage error(△) is calculated using the following Equation [22]:(9)Δ=yexp−ypredyexp×100%.Table 9
Comparison of the measured and predicted value.
No.Surface roughness (Ra)Surface microhardness (HV)Ra (μm) expRSM predANN predError (%) (RSM)Error (%) (ANN)HV (%) expRSM predANN predError (%) (RSM)Error (%) (ANN)11.361.44831.34146.491.37455480.1878455.84145.540.1820.790.76930.79192.620.24435443.4931434.54981.950.1031.281.44831.341413.154.80460480.1878455.84144.390.9040.70.83620.728919.454.12438503.8056437.63415.020.0850.680.88420.682830.020.41440445.1016439.84751.160.0362.512.48432.65081.025.61449514.1188447.080414.500.4372.172.23721.94513.1010.37450487.6745461.88178.372.6480.740.76290.74443.100.60456482.2466455.33195.760.1591.812.11771.815117.000.28412473.7475410.657914.990.33101.351.42211.35975.340.72440476.2698454.1628.243.22111.321.44831.34149.721.62458480.1878455.84144.840.47121.21.44831.341420.6911.78449480.1878455.84146.951.52130.830.96130.834715.820.57421487.6771418.874515.840.50141.581.51131.58474.350.30426440.0838434.13043.311.91151.371.51131.381510.310.84420484.2918418.274515.310.41162.322.43632.32265.010.11480484.4068479.36560.920.13171.451.44831.34140.127.49452480.1878455.84146.240.85181.531.54801.43741.176.05468495.6513462.10115.911.26191.211.44831.341419.6910.86448480.1878455.84147.181.75202.272.30972.30471.751.53426429.5155425.7280.830.06Average9.503.487.360.85Figure 7
Experimental, RSM, and ANN predicted results forRa.Figure 8
Experimental, RSM, and ANN predicted results forHV.For RSM and ANN, the maximum test errors for surface roughness are about 30.02% and 11.78%, respectively. The mean absolute percentage error between RSM and experimental values can be seen as 9.50%, whereas the same value is only 3.48% with the ANN model. In surface microhardness, the same maximum test errors for RSM and ANN are revealed as 15.84% and 3.22%, respectively. The mean absolute percentage errors between experimental and estimated by RSM and ANN are found to be 7.36% and 0.85%. Actual values and anticipated values for ANN and RSM are shown in Figures7 and 8. Thus, it can be seen that ANN is closer to the test results than RSM, showing a better fitting effect.


## 5. Optimization with DFA

One of the most popular approaches for manufacturing’s multiple response process optimizations is the desire function approach (DFA) [28, 29]. A typical way is the desirability approach, which allocates a “score” to a collection of replies and selects factor settings that maximizes that score. To find out the maximum and minimum of the target goal, the desirability can be defined from the following Equations:(10)di=0,ifyi,p≤yi,p,min,yi,p,max−yi,pyi,p,max−yi,p,min,ifyi,p,min≤yi,p≤yi,p,max,1,ifyi,p≥yi,p,max,(11)di=0,ifyi,p≤yi,p,min,yi,p−yi,p,minyi,p,max−yi,p,min,ifyi,p,min≤yi,p≤yi,p,max,1,ifyi,p≥yi,p,max,(12)Descomb=∏i=1ndi1/n,where, di is the individual desirability and yi,p is the response, yi,p,max andyi,p,min are the max and the min values of the response. n is the number of responses. Descomb is the composite desirability, which gets all goals combined into one desirability function.According to the previous analysis, ANN models with reliable predictability are used to evaluate individual desirability. It is expected that the individual desirability of surface roughness is smaller the better and surface microhardness is larger the better, which were calculated by Equations (10) and (11) respectively. Table 10 shows the evaluated individual and composite desirability, as well as their rank for (Ra) and (HV). The optimization parameters are vc2-f1-ap2, which are cutting speed = 60 m/min, feed rate = 0.06 mm/r, and cutting depth = 0.2 mm with estimated Ra = 0.7444um and surface microhardness HV =455.3319.Table 10
Expectation assessment forRa and HV.
Runs.ANN predicted value (yi,p)Individual desirability (di)Composite desirabilityRankRaHVRa (%)HV (%)(Descomb) (%)11.3414455.84140.66540.65760.6615320.7919434.54980.94460.34770.57311231.3414455.84140.66540.65760.6615340.7289437.63400.97660.39260.61921150.6828439.84751.00000.42480.6518962.6508447.08040.00000.53010.00001971.9451461.88170.35860.74550.51711380.7444455.33190.96870.65020.7936191.8151410.65790.42460.00000.000019101.3597454.16200.65600.63320.644510111.3414455.84140.66540.65760.66153121.3414455.84140.66540.65760.66153130.8347418.87450.92280.11960.332216141.5847434.13040.54170.34160.430214151.3815418.27450.64500.11090.267417162.3226479.36560.16681.00000.408415171.3414455.84140.66540.65760.66153181.4374462.10110.61660.74870.67952191.3414455.84140.66540.65760.66153202.3047425.72800.17590.21930.196418


## 6. Confirmation Test

To verify the reliability of the optimization results, the optimized parameters ofvc2-f1-ap2 were selected for the confirmation experiment (seen in Table 11). The surface roughness and surface microhardness obtained by the test were 0.751 μm and 468.2. The error rates are about 0.89% and 2.83% between the predicted and experimental, which can prove the reliability of the optimization results.Table 11
Confirmation of optimization results.
ResponsesPredictedExperimentalError (%)(vc2-f1-ap2)(vc2-f1-ap2)Ra (μm)0.74440.7510.89HV455.3319468.22.83


## 7. Conclusions

In this paper, the predicted models of surface roughness and surface microhardness are established using RSM and ANN techniques in the TC17 turning experiment based on the Box-Behnken design, and the following conclusions can be obtained:(1)
From the ANOVA analysis, feed rate with 91.67% contributions has the most important influence on the surface roughness (Ra) and cutting depth with 16.56% contributions occupies the first position in influencing the quality of surface microhardness (HV).(2)
The ANN prediction models of surface roughness (R2 = 99.99%) and surface microhardness (R2 = 99.23%) have higher prediction accuracy and small error than the RSM prediction models of surface roughness (R2 = 97.62%) and surface microhardness (R2 = 93.31%).(3)
The mean absolute percentage errors forRa and HV between experimental and estimated by ANN can be only 3.48% and 0.85%, which are smaller than 9.50% and 7.36% estimated by RSM.(4)
The optimization parameters with minimum surface roughness and maximize surface microhardness are cutting speed 60 m/min, feed rate 0.06 mm/r, and cutting depth 0.2 mm, which were obtained with the DFA technique. In the confirmed experiment, the errors ofRa and HV between ANN predicted and the experiment are 0.89% and 2.83%.



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*Source: 2979858-2022-10-05.xml*