# Multiobjective Optimization of Milling Parameters for Ultrahigh-Strength Steel AF1410 Based on the NSGA-II Method

Authors: Jin Xu; Fuwu Yan; Yan Li; Zhenchao Yang; Long Li
Journal: Advances in Materials Science and Engineering
 (2020)

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## Abstract

In this paper, ultrahigh-strength steel AF1410 was milled with the carbide tool, and a total of thirty experiments were performed based on central composite design (CCD) of response surface methodology. The prediction models of milling force and surface roughness are established, respectively. The influence of milling parameters (milling speed, each tooth feed, radial depth of cut, and axial depth of cut) on milling force and surface roughness is studied by ANOVA and established prediction model. Multiobjective optimization of milling parameters is accomplished based on nondominated sorting genetic algorithm II (NSGA-II) with milling force, surface roughness, and material removal rate as optimization objectives. The surface roughness, cutting force, and material removal rate are important indexes to measure the energy consumed in the process of product, the surface machining quality, and machining efficiency of processing, respectively. In order to minimize milling force and surface roughness and maximize material removal rate, NSGA-II was used for multiobjective optimization to obtain the optimal fitness value of the objective function. The NSGA-II has been applied to obtain a set of optimal combination of parameters from the Pareto-optimal solution set to enhance the machining conditions.


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## Body

## 1. Introduction

Ultrahigh-strength steel has the characteristics of high strength and high toughness, which is one of the preferred materials for the important load-bearing components of ships, aviation aircraft, and military equipment [1]. However, from the viewpoint of manufacturability, the ultrahigh-strength steel generally has the characteristics of hard mass and poor thermal conductivity [2–4]. So, it is difficult to perform cutting processing [5].To solve the problem of hard machining of ultrahigh-strength steel, the key is to study the cutting mechanism and select the reasonable process parameter [6, 7]. Among them, cutting force, surface roughness, and material removal rate are important physical quantities in the cutting process, which has an important influence on the energy consumed in the process of product, the surface quality, and machining efficiency of processing [8–11]. Therefore, cutting force and surface roughness have always been the key research target in cutting mechanism research, and they are also the basic indexes for evaluating cutting process parameters. Unreasonable cutting parameters lead to large cutting force, poor surface quality, and low machining efficiency. Therefore, it is necessary to select reasonable cutting parameters with the objectives of minimum surface roughness, minimum milling force, and maximum material removal rate.Machining parameter optimization is one of the most effective methods to reduce machining cost and improve quality and efficiency in the field of machining [12, 13]. Material removal rate, cutting force, and surface roughness are conflicting, and the optimization of one target will cause other targets to become worse. In order to solve this problem, multiobjective parameter optimization is carried out to obtain the optimal fitness value of the objective function [14–16].Masmati et al. [17] studied the end milling on S50C medium carbon steel, obtained the quadratic polynomial regression equation of residual stress, milling force, and surface roughness by the RSM, and discussed the influence of primary and interactive cutting parameters on residual stress milling force and surface roughness. Orra and Choudhury [18] studied the influence of chip formation, cutting tip radius, and tool wear on cutting force. The orthogonal experiments of turning two different materials AISI 52100 steel and AISI 4340 steel were carried out, and the prediction model of three-way cutting force was obtained. Patel et al. [19] conducted an end milling study on AISI 304 stainless steel. The effects of spindle speed, feed speed, and cutting depth on the cutting force and surface roughness were studied by the Taguchi method. Then, the optimal process parameter combination was obtained with the optimization of the minimum surface roughness and cutting force. Chatterjee et al. [20] studied the drilling of hole on AISI304 stainless steel and analyzed the influence of drilling parameters, i.e., spindle speed, feed rate, and drill bit diameter, on burr height and circularity and optimization of boring parameters using nondominated sorting genetic algorithm (NSGA). Ajith Arul Daniel et al. [21] studied the drilling of aluminium metal matrix composites and conducted drilling experiments based on Taguchi L27 orthogonal design. The drilling parameters of aluminium metal matrix composites were optimized by using NSGA-II to maximize the material removal rate (MRR) and minimize the temperature. Sur and Erkan [22] studied the drilling of carbon fiber reinforced plastic (CFRP) composite plates, the Taguchi experimental design was selected, the influence rates of different cutting parameters and drill geometry on the damage factor were discussed by ANOVA, and the cutting parameters are optimized to minimize the delamination damage in the drilling. Kara [23] studied the turning of DIN 1.2344 hot work tool steel, obtained the surface roughness (Ra) and the flank wear (Vb) of different machining parameters by the Taguchi method, and established a quadratic regression model. The optimal Ra and Vb values were determined by Taguchi optimization. ANOVA results showed that the most important parameters affecting Ra and Vb were feed rate. Singh et al. [24] studied the influence of the machining parameters during milling upon the surface roughness (SR) and material removal rate (MRR) of AISI H11 steel and investigated the relationship between surface roughness (SR) and material removal rate (MRR) by Taguchi grey relational analysis (TGRA) with standard L27 orthogonal array (OA). The model significance tests have been conducted by the ANOVA method: cutting speed contributes the most to finish machining and feed rate contributes the most to rough machining. Erkan et al. [25] carried out milling research on glass-fiber reinforced polymer composite (GFRP) materials, analyzed the relationship between the cutting parameters and the surface roughness in end milling, and used the Taguchi method and genetically optimized neural network systems (GONNs) for data analysis and selection of optimal cutting parameters. Ozturk and Kara [26] carried out a study on the machinability of 6061 aluminium alloy. According to Taguchi design experiment, cutting speeds, feed rates, cutting depths, and two different cooling methods were selected as experimental indexes, and cutting parameters were optimized to achieve minimum surface roughness (Ra) and energy consumption (EC). Kara [27] studied the performance of cutting parameters used in the finish milling of the AISI P20+S plastic-mold steel and determined the optimum machining conditions. Control factors for the optimum surface roughness values were determined by the Taguchi method, and the influence of control factors on surface roughness was analyzed by ANOVA.AF1410 steel is a kind of high strength and high toughness secondary hardening steel, which has good welding performance and excellent corrosion resistance [28, 29]. It is widely used in the manufacture of military equipment such as submarines, military aircraft, and artillery. At present, the research on the AF1410 steel focuses on the material composition design, mechanical property optimization, heat treatment, and welding process [30, 31]. There are few research studies on process parameters by multiobjective optimization for AF1410 steel.In order to fill this literature gap, this study aims to determine the optimal combination of milling parameters that will be contributive to achieving the minimum milling forces, minimum surface roughness, and maximum material removal rate. In this paper, firstly, the milling force and surface roughness of AF1410 steel under different milling parameters are obtained by the peripheral milling test. Then, the RSM is used to establish the prediction model of milling forces and surface roughness in the milling process of the AF1410 steel. Next, the influences of each milling parameter on the milling forces and surface roughness are analyzed by using ANOVA and regression model. Finally, with the objectives of minimum milling force, minimum surface roughness, and maximum material removal rate, NSGA-II is used for multiobjective parameter optimization to obtain the optimal fitness value of the objective function.


## 2. Materials and Methods

### 2.1. Material Characteristics

The chemical composition of the material was obtained by spectroscopic analysis. The chemical composition of AF1410 steel used in this study is shown in Table1. The material adopts forging blank. The preprocessing heat treatment process of the material is high temperature tempering after normalizing. The hardness of the material is HRC38-39.Table 1
Chemical composition (wt.%) of AF1410 steel.
ElementCCoNiCrMoSiMnPSwt.%0.1613.839.931.951.040.010.020.0060.001The uniaxial tensile test was used to obtain the basic mechanical parameters of the material. The tensile test equipment is a 100 kN mechanical testing machine (MTS Inc., Eden Prairie, MN, USA). The mechanical properties of AF1410 steel are listed in Table2. It is noted that the AF1410 steel has high strength and certain percentage elongation, which makes machining difficult.Table 2
Mechanical properties of AF1410 steel.
Tensile strength (MPa)Yield strength (MPa)Elongation rate (%)Surface shrinkage (%)162014801260


### 2.2. Methods

The experimental method is to establish the functional relationship between the measured object and the related variables by using the statistical principle [32]. Response surface methodology (RSM) is a statistical test method used for developing, improving, and optimizing. RSM was widely used in the establishment of prediction model and the optimization of cutting parameters in machining [33]. Ic et al. [34] used the Box–Behnken method to design experiments, took carbon emission and surface roughness in turning as optimization objectives, and established a regression model with response surface method to optimize turning parameters. Mia et al. [35] used response optimization technique to investigate the influence of machining parameters on the quality of surface produced in end milling of hardened AISI 4140 steel under the MQL. Mia [36] used carbide cutter to perform the end milling test on AISI 4140 steel after quenching under the condition of drying and minimum lubrication, and the predictive model of the responses was formulated by using response surface methodology.The above studies show that experiment research can reflect the relationship between process parameters and response value more accurately and intuitively. Therefore, experiment research plays an irreplaceable role in modeling and optimization of cutting force and surface roughness. The response surface method is used for modeling and analyzing the influence of cutting parameters on the cutting process, but it cannot deal with the multiresponse problem, and multiobjective optimization can obtain the optimal parametric combination.


#### 2.2.1. RSM Equations

RSM is the most widely used mathematical modeling for establishing empirical formula, which can predict and explain the relationship between the input parameters and the responses (dependent variables) [37, 38]. In addition, this method can easily find out the quantitative law between the test index and each factor intuitively and get the best combination of each factor level according to the index requirement [39]. The response surface method must have enough test data and determine a suitable response surface mathematical model. In order to reduce the cost and the amount of experiment, the most commonly experimental design methods for the RSM are CCD and Box-Behnken design (BBD) [40]. Compared with the number of experiments required by the conventional methods, only few and efficient experiments are done in these experimental design methods. Generally, the second-order polynomial or exponential function is used as the mathematical model of the response surface.In this study, the second-order polynomial equation is used as the mathematical model of the response surface. The general form of this equation is shown in the following formula:(1)y=β0+βi∑i=1nxi+βij∑i<jxixj+βii∑i=1nxi2+ε,where y is the response value; n is the number of factors; β0 is a constant; βi, βii, and βij are constants to the first-degree factor, the second-degree factor, and factor interactions, respectively; xi is the value of the ith factor; and ε is the residual (experimental error).


#### 2.2.2. Experimental Equipment and Conditions

The experiment was carried out on a HAAS-VF1 vertical machining center (HAAS Inc., Oxnard, CA, USA) having 15 kW motor power and maximum 30000 rpm spindle. The tool used in the study is a 4-edge end mill H4020017-10-1 (Walter Inc., Tubingen, Germany) made of carbide. Milling force sensor is 9257B three-way dynamic piezoelectric force sensor (Kistler Inc., Shanghai, China). The signal system consists of 5070A charge amplifier (Kistler Inc., Shanghai, China) and data acquisition instrument, WS-5921 (Wavespectrum Inc., Beijing, China). Surface roughness is measured with surface roughness measuring instrument, RC50H (VALE Inc., Xi’an, Shaanxi, China). The material is made into workpieces for milling experiment by wire-electrode cutting and grinding. The experimental equipment is shown in Figure1.Figure 1
Experimental equipment and measuring equipment.


#### 2.2.3. Experimental Design and Steps

The selection of design parameters is the key link of experimental design. In this study, the CCD method is used to design experiments. The milling speedvc, feed per tooth fz, axial depth of cut ap, and radial depth of cut ae are chosen as independent variables, and each independent variable takes three levels, respectively. The values of the experimental independent variables and their corresponding levels are shown in Table 3.Table 3
Independent variables and the levels.
Independent variablesLevels−101Milling speedvc (m/min)12.5618.8425.12Feed per toothfz (mm/z)0.020.040.06Axial depth of cutap (mm)135Radial depth of cutae (mm)0.51.252The selection of machining parameter range is based on the suggested reference range provided by the tool manufacturer. It should be pointed out that the change of milling speed in the actual test is realized by controlling the spindle rotation speed. In order to make the results more universal, the milling speed is based on cutting edge line speed m/min instead of the spindle speed rpm, which makes the result not limited to the tool radius size used in this paper. For the same reason, feed per tooth is selected as a research factor rather than the actual feed speed of the workpieces.According to the requirements of experimental design, 30 groups of experiments need to be carried out, and Table4 shows the combination of parameters implemented in each group of experiments. Milling methods are peripheral milling (down milling) and emulsion cooling. Tools are checked and replaced after each experiment. The x-direction, y-direction, and z-direction milling forces Fx, Fy, and Fz are experimental values. Each direction milling force is measured. And the values of Fx, Fy, and Fz are obtained by averaging 50 consecutive peaks of each direction milling force. The coordinate system is shown in Figure 1. The total milling force is the response value, and the expression of the total milling force is shown in the following formula:(2)Ft=Fx2+Fy2+Fz2,where Ra is used as surface roughness parameter value. The Surftest is set to a cutoff length of 0.8 mm and sampling length of 4.8 mm. Ra is measured in the transverse direction of the sampling centerline. Each Ra measurement is repeated at least three times, and average of three Ra values is recorded.Table 4
Experimental scheme and results.
Number of testsProcess parameterMilling forceFt (N)Surface roughnessRa (μm)Material removal rate MRR (mm3/min)vc (m/min)fz (mm/z)ap (mm)ae (mm)112.560.065.002.00488.090.682960212.560.061.000.5096.050.39248312.560.043.001.25292.280.466240412.560.025.002.00329.770.423320512.560.021.000.5061.520.27616612.560.025.000.50136.800.23180712.560.061.002.00227.600.512192812.560.021.002.00141.340.38564912.560.065.000.50196.680.3422401018.840.063.001.25347.300.4085401118.840.043.002.00349.550.3675761218.840.041.001.25140.820.3521201318.840.023.001.25235.010.3131801418.840.043.001.25285.400.3393601518.840.043.001.25291.260.3613601618.840.043.001.25284.860.3563601718.840.043.000.50153.490.2371441818.840.043.001.25287.740.3263601918.840.043.001.25289.110.3363602018.840.043.001.25290.990.3243602118.840.045.001.25279.930.3446002225.120.021.002.00133.710.2461282325.120.021.000.5062.350.223322425.120.065.002.00457.930.34819202525.120.025.000.50135.080.1651602625.120.065.000.50180.020.1894802725.120.061.002.00212.500.2813842825.120.043.001.25269.520.2554802925.120.061.000.5097.930.292963025.120.025.002.00316.300.261640The material removal rate (MRR) is the volume of the workpiece material removed in a unit time. For milling, MRR is expressed as the product of spindle speedn, feed per tooth fz, tool tooth number z, axial depth of cut ap, and radial depth of cut ae. According to the experimental setting of processing parameters, the expression of material removal rate is shown in formula (3). In the formula, the parameter d is the tool diameter.(3)MRR=1000vcfzzapaeπd.


## 2.1. Material Characteristics

The chemical composition of the material was obtained by spectroscopic analysis. The chemical composition of AF1410 steel used in this study is shown in Table1. The material adopts forging blank. The preprocessing heat treatment process of the material is high temperature tempering after normalizing. The hardness of the material is HRC38-39.Table 1
Chemical composition (wt.%) of AF1410 steel.
ElementCCoNiCrMoSiMnPSwt.%0.1613.839.931.951.040.010.020.0060.001The uniaxial tensile test was used to obtain the basic mechanical parameters of the material. The tensile test equipment is a 100 kN mechanical testing machine (MTS Inc., Eden Prairie, MN, USA). The mechanical properties of AF1410 steel are listed in Table2. It is noted that the AF1410 steel has high strength and certain percentage elongation, which makes machining difficult.Table 2
Mechanical properties of AF1410 steel.
Tensile strength (MPa)Yield strength (MPa)Elongation rate (%)Surface shrinkage (%)162014801260


## 2.2. Methods

The experimental method is to establish the functional relationship between the measured object and the related variables by using the statistical principle [32]. Response surface methodology (RSM) is a statistical test method used for developing, improving, and optimizing. RSM was widely used in the establishment of prediction model and the optimization of cutting parameters in machining [33]. Ic et al. [34] used the Box–Behnken method to design experiments, took carbon emission and surface roughness in turning as optimization objectives, and established a regression model with response surface method to optimize turning parameters. Mia et al. [35] used response optimization technique to investigate the influence of machining parameters on the quality of surface produced in end milling of hardened AISI 4140 steel under the MQL. Mia [36] used carbide cutter to perform the end milling test on AISI 4140 steel after quenching under the condition of drying and minimum lubrication, and the predictive model of the responses was formulated by using response surface methodology.The above studies show that experiment research can reflect the relationship between process parameters and response value more accurately and intuitively. Therefore, experiment research plays an irreplaceable role in modeling and optimization of cutting force and surface roughness. The response surface method is used for modeling and analyzing the influence of cutting parameters on the cutting process, but it cannot deal with the multiresponse problem, and multiobjective optimization can obtain the optimal parametric combination.


### 2.2.1. RSM Equations

RSM is the most widely used mathematical modeling for establishing empirical formula, which can predict and explain the relationship between the input parameters and the responses (dependent variables) [37, 38]. In addition, this method can easily find out the quantitative law between the test index and each factor intuitively and get the best combination of each factor level according to the index requirement [39]. The response surface method must have enough test data and determine a suitable response surface mathematical model. In order to reduce the cost and the amount of experiment, the most commonly experimental design methods for the RSM are CCD and Box-Behnken design (BBD) [40]. Compared with the number of experiments required by the conventional methods, only few and efficient experiments are done in these experimental design methods. Generally, the second-order polynomial or exponential function is used as the mathematical model of the response surface.In this study, the second-order polynomial equation is used as the mathematical model of the response surface. The general form of this equation is shown in the following formula:(1)y=β0+βi∑i=1nxi+βij∑i<jxixj+βii∑i=1nxi2+ε,where y is the response value; n is the number of factors; β0 is a constant; βi, βii, and βij are constants to the first-degree factor, the second-degree factor, and factor interactions, respectively; xi is the value of the ith factor; and ε is the residual (experimental error).


### 2.2.2. Experimental Equipment and Conditions

The experiment was carried out on a HAAS-VF1 vertical machining center (HAAS Inc., Oxnard, CA, USA) having 15 kW motor power and maximum 30000 rpm spindle. The tool used in the study is a 4-edge end mill H4020017-10-1 (Walter Inc., Tubingen, Germany) made of carbide. Milling force sensor is 9257B three-way dynamic piezoelectric force sensor (Kistler Inc., Shanghai, China). The signal system consists of 5070A charge amplifier (Kistler Inc., Shanghai, China) and data acquisition instrument, WS-5921 (Wavespectrum Inc., Beijing, China). Surface roughness is measured with surface roughness measuring instrument, RC50H (VALE Inc., Xi’an, Shaanxi, China). The material is made into workpieces for milling experiment by wire-electrode cutting and grinding. The experimental equipment is shown in Figure1.Figure 1
Experimental equipment and measuring equipment.


### 2.2.3. Experimental Design and Steps

The selection of design parameters is the key link of experimental design. In this study, the CCD method is used to design experiments. The milling speedvc, feed per tooth fz, axial depth of cut ap, and radial depth of cut ae are chosen as independent variables, and each independent variable takes three levels, respectively. The values of the experimental independent variables and their corresponding levels are shown in Table 3.Table 3
Independent variables and the levels.
Independent variablesLevels−101Milling speedvc (m/min)12.5618.8425.12Feed per toothfz (mm/z)0.020.040.06Axial depth of cutap (mm)135Radial depth of cutae (mm)0.51.252The selection of machining parameter range is based on the suggested reference range provided by the tool manufacturer. It should be pointed out that the change of milling speed in the actual test is realized by controlling the spindle rotation speed. In order to make the results more universal, the milling speed is based on cutting edge line speed m/min instead of the spindle speed rpm, which makes the result not limited to the tool radius size used in this paper. For the same reason, feed per tooth is selected as a research factor rather than the actual feed speed of the workpieces.According to the requirements of experimental design, 30 groups of experiments need to be carried out, and Table4 shows the combination of parameters implemented in each group of experiments. Milling methods are peripheral milling (down milling) and emulsion cooling. Tools are checked and replaced after each experiment. The x-direction, y-direction, and z-direction milling forces Fx, Fy, and Fz are experimental values. Each direction milling force is measured. And the values of Fx, Fy, and Fz are obtained by averaging 50 consecutive peaks of each direction milling force. The coordinate system is shown in Figure 1. The total milling force is the response value, and the expression of the total milling force is shown in the following formula:(2)Ft=Fx2+Fy2+Fz2,where Ra is used as surface roughness parameter value. The Surftest is set to a cutoff length of 0.8 mm and sampling length of 4.8 mm. Ra is measured in the transverse direction of the sampling centerline. Each Ra measurement is repeated at least three times, and average of three Ra values is recorded.Table 4
Experimental scheme and results.
Number of testsProcess parameterMilling forceFt (N)Surface roughnessRa (μm)Material removal rate MRR (mm3/min)vc (m/min)fz (mm/z)ap (mm)ae (mm)112.560.065.002.00488.090.682960212.560.061.000.5096.050.39248312.560.043.001.25292.280.466240412.560.025.002.00329.770.423320512.560.021.000.5061.520.27616612.560.025.000.50136.800.23180712.560.061.002.00227.600.512192812.560.021.002.00141.340.38564912.560.065.000.50196.680.3422401018.840.063.001.25347.300.4085401118.840.043.002.00349.550.3675761218.840.041.001.25140.820.3521201318.840.023.001.25235.010.3131801418.840.043.001.25285.400.3393601518.840.043.001.25291.260.3613601618.840.043.001.25284.860.3563601718.840.043.000.50153.490.2371441818.840.043.001.25287.740.3263601918.840.043.001.25289.110.3363602018.840.043.001.25290.990.3243602118.840.045.001.25279.930.3446002225.120.021.002.00133.710.2461282325.120.021.000.5062.350.223322425.120.065.002.00457.930.34819202525.120.025.000.50135.080.1651602625.120.065.000.50180.020.1894802725.120.061.002.00212.500.2813842825.120.043.001.25269.520.2554802925.120.061.000.5097.930.292963025.120.025.002.00316.300.261640The material removal rate (MRR) is the volume of the workpiece material removed in a unit time. For milling, MRR is expressed as the product of spindle speedn, feed per tooth fz, tool tooth number z, axial depth of cut ap, and radial depth of cut ae. According to the experimental setting of processing parameters, the expression of material removal rate is shown in formula (3). In the formula, the parameter d is the tool diameter.(3)MRR=1000vcfzzapaeπd.


## 2.2.1. RSM Equations

RSM is the most widely used mathematical modeling for establishing empirical formula, which can predict and explain the relationship between the input parameters and the responses (dependent variables) [37, 38]. In addition, this method can easily find out the quantitative law between the test index and each factor intuitively and get the best combination of each factor level according to the index requirement [39]. The response surface method must have enough test data and determine a suitable response surface mathematical model. In order to reduce the cost and the amount of experiment, the most commonly experimental design methods for the RSM are CCD and Box-Behnken design (BBD) [40]. Compared with the number of experiments required by the conventional methods, only few and efficient experiments are done in these experimental design methods. Generally, the second-order polynomial or exponential function is used as the mathematical model of the response surface.In this study, the second-order polynomial equation is used as the mathematical model of the response surface. The general form of this equation is shown in the following formula:(1)y=β0+βi∑i=1nxi+βij∑i<jxixj+βii∑i=1nxi2+ε,where y is the response value; n is the number of factors; β0 is a constant; βi, βii, and βij are constants to the first-degree factor, the second-degree factor, and factor interactions, respectively; xi is the value of the ith factor; and ε is the residual (experimental error).


## 2.2.2. Experimental Equipment and Conditions

The experiment was carried out on a HAAS-VF1 vertical machining center (HAAS Inc., Oxnard, CA, USA) having 15 kW motor power and maximum 30000 rpm spindle. The tool used in the study is a 4-edge end mill H4020017-10-1 (Walter Inc., Tubingen, Germany) made of carbide. Milling force sensor is 9257B three-way dynamic piezoelectric force sensor (Kistler Inc., Shanghai, China). The signal system consists of 5070A charge amplifier (Kistler Inc., Shanghai, China) and data acquisition instrument, WS-5921 (Wavespectrum Inc., Beijing, China). Surface roughness is measured with surface roughness measuring instrument, RC50H (VALE Inc., Xi’an, Shaanxi, China). The material is made into workpieces for milling experiment by wire-electrode cutting and grinding. The experimental equipment is shown in Figure1.Figure 1
Experimental equipment and measuring equipment.


## 2.2.3. Experimental Design and Steps

The selection of design parameters is the key link of experimental design. In this study, the CCD method is used to design experiments. The milling speedvc, feed per tooth fz, axial depth of cut ap, and radial depth of cut ae are chosen as independent variables, and each independent variable takes three levels, respectively. The values of the experimental independent variables and their corresponding levels are shown in Table 3.Table 3
Independent variables and the levels.
Independent variablesLevels−101Milling speedvc (m/min)12.5618.8425.12Feed per toothfz (mm/z)0.020.040.06Axial depth of cutap (mm)135Radial depth of cutae (mm)0.51.252The selection of machining parameter range is based on the suggested reference range provided by the tool manufacturer. It should be pointed out that the change of milling speed in the actual test is realized by controlling the spindle rotation speed. In order to make the results more universal, the milling speed is based on cutting edge line speed m/min instead of the spindle speed rpm, which makes the result not limited to the tool radius size used in this paper. For the same reason, feed per tooth is selected as a research factor rather than the actual feed speed of the workpieces.According to the requirements of experimental design, 30 groups of experiments need to be carried out, and Table4 shows the combination of parameters implemented in each group of experiments. Milling methods are peripheral milling (down milling) and emulsion cooling. Tools are checked and replaced after each experiment. The x-direction, y-direction, and z-direction milling forces Fx, Fy, and Fz are experimental values. Each direction milling force is measured. And the values of Fx, Fy, and Fz are obtained by averaging 50 consecutive peaks of each direction milling force. The coordinate system is shown in Figure 1. The total milling force is the response value, and the expression of the total milling force is shown in the following formula:(2)Ft=Fx2+Fy2+Fz2,where Ra is used as surface roughness parameter value. The Surftest is set to a cutoff length of 0.8 mm and sampling length of 4.8 mm. Ra is measured in the transverse direction of the sampling centerline. Each Ra measurement is repeated at least three times, and average of three Ra values is recorded.Table 4
Experimental scheme and results.
Number of testsProcess parameterMilling forceFt (N)Surface roughnessRa (μm)Material removal rate MRR (mm3/min)vc (m/min)fz (mm/z)ap (mm)ae (mm)112.560.065.002.00488.090.682960212.560.061.000.5096.050.39248312.560.043.001.25292.280.466240412.560.025.002.00329.770.423320512.560.021.000.5061.520.27616612.560.025.000.50136.800.23180712.560.061.002.00227.600.512192812.560.021.002.00141.340.38564912.560.065.000.50196.680.3422401018.840.063.001.25347.300.4085401118.840.043.002.00349.550.3675761218.840.041.001.25140.820.3521201318.840.023.001.25235.010.3131801418.840.043.001.25285.400.3393601518.840.043.001.25291.260.3613601618.840.043.001.25284.860.3563601718.840.043.000.50153.490.2371441818.840.043.001.25287.740.3263601918.840.043.001.25289.110.3363602018.840.043.001.25290.990.3243602118.840.045.001.25279.930.3446002225.120.021.002.00133.710.2461282325.120.021.000.5062.350.223322425.120.065.002.00457.930.34819202525.120.025.000.50135.080.1651602625.120.065.000.50180.020.1894802725.120.061.002.00212.500.2813842825.120.043.001.25269.520.2554802925.120.061.000.5097.930.292963025.120.025.002.00316.300.261640The material removal rate (MRR) is the volume of the workpiece material removed in a unit time. For milling, MRR is expressed as the product of spindle speedn, feed per tooth fz, tool tooth number z, axial depth of cut ap, and radial depth of cut ae. According to the experimental setting of processing parameters, the expression of material removal rate is shown in formula (3). In the formula, the parameter d is the tool diameter.(3)MRR=1000vcfzzapaeπd.


## 3. Results and Discussion

### 3.1. Results and Regression Model

Specific experimental scheme and results are shown in Table4.The mathematical relation between the control parameters and the output responses is developed using nonlinear second-order regression equation (1). Finally, the regression model describes the process parameters and milling force; the process parameters and surface roughness are given in Table 5.Table 5
Regression models andR2 values.
Regression modelsR2Ft=−54.3−1.18vc−2429fz+104.2ap+129.0ae−18.9vcfz−0.209vcap−0.673vcae+265fzap+1209fzae+22.76apae+0.066vc2+32117fz2−16.98ap2−47.6ae20.9940Ra=0.227−0.0072vc+1.89fz−0.0203ap+0.3075ae−0.198vcfz−0.000955vcap−0.00656vcae+0.209fzap+0.783fzae+0.02275apae+0.000355vc2+35fz2+0.00037ap2−0.0791ae20.9719The model prediction ability is commonly measured by the value of termR2. R2 value greater than 0.9 indicates that all the predicted values obtained by the regression model are within reliable interval. R2 values of regression models of Ft and Ra are 0.9940 and 0.9719, respectively. Figure 2 shows the correlation of the experimental milling forces and the predicted values obtained from the regression model, in which the position of the points is determined by the experimental value and predicted value of the same process parameter combination. The closeness of these points with the linear curves (y = x) indicates how compatible the predicted values are with the actual values. It can be seen that the distribution of points tends to be linear (y = x), suggesting that the results have no large deviation. Therefore, it is sufficient to say that the milling force and surface roughness regression model established by the response surface method are effective.Figure 2
Correlation of predicted values versus experimental values: (a)Ft; (b) Ra.
(a)(b)


### 3.2. Significance Test of Process Parameters

ANOVA is used to judge the significance of each factor to the responses. ANOVA results are listed in Table6. P value of P<0.05 (5% importance value) indicates a statistically significant effect of the parameters or interaction on the response value. F value of the parameters or interaction indicates the contribution of the source to the response value, and the greater the F value, the greater the contribution of the factor to the response value.Table 6
The ANOVA forFt and Ra.
SourceFtRaFPRemarksFPRemarksvc4.530.0503205.58<0.0001✓fz233.46<0.0001✓83.42<0.0001✓ap748.38<0.0001✓0.0660.8005ae974.55<0.0001✓131.3<0.0001✓vcfz0.670.425217.450.0008✓vcap0.820.37994.060.0622vcae1.190.29226.880.0001✓fzap13.350.0023✓1.980.18fzae39.06<0.0001✓3.890.0672apae138.48<0.0001✓32.84<0.0001✓vc20.130.72420.890.3594fz23.180.0950.890.3594ap288.8<0.0001✓0.010.9211ae213.810.0021✓9.050.0088✓Accordingly, forFt, the most effective parameter is seen to be ae, followed by ap and fz. vc has no significant effect on Ft. For Ra, the most effective parameter is seen to be vc, followed by ae and fz. ap has no significant effect on Ra. Moreover, the quadratic effect of ap2 as well as the interaction of ap and ae has the most influential contribution to Ft. And the quadratic effect of ae2 as well as the interaction of ap and ae has the most influential contribution to Ra.In the given ANOVA tables, besides the remarked effective parameters, the other parameters also have some effects that can be found from theirF value. But these effects are relatively weak and can be neglected in analysis.


### 3.3. Response Surfaces and Analysis

According to the regression model in Table5, taking two process parameters as variables and keeping the other two process parameters at 0 level, we can obtain the three-dimensional (3D) response surface in which the cutting force varies with these two process parameters. Figures 3 and 4 present the 3D response surfaces on milling force and surface roughness by variable factors, respectively. Through the 3D response surfaces, the influence of each process parameter and its interaction on milling force and surface roughness can be seen intuitively.Figure 3
3D response surfaces onFt: (a) vc − fz; (b) vc − ap; (c) vc − ae; (d) fz − ap; (e) fz − ae; (f) ap − ae.
(a)(b)(c)(d)(e)(f)Figure 4
3D response surfaces onRa: (a) vc − fz; (b) vc − ap; (c) vc − ae; (d) fz − ap; (e) fz − ae; (f) ap − ae.
(a)(b)(c)(d)(e)(f)The effects ofvc on Ft seem to be remarkably weak, as shown in Figures 3(a)–3(c). Ft has a small reduction with the increase of vc. As the milling speed increases, the milling temperature increases and the friction coefficient decreases. Meanwhile, the shear angle increases and the shear area decreases. So, the decreasing Ft, as a result of decreased friction and shear area, is an anticipated outcome.From Figure3, the milling force increases with the increment of fz, ap, and ae. From the characteristics of circumferential milling process, it can be seen that the cutting thickness per tooth increases with the increase of feed per tooth and the milling area increases with the increase of axial depth of cut and radial depth of cut. The generally accepted theory for calculating milling forces is that milling forces are positively correlated to the fz, ap, and ae. Therefore, from the point of view of the influence of single factor on milling force, reducing fz, ap, and ae is helpful to reduce milling forces.From Figures4(b), 4(d), and 4(f), the effects of ap on Ra seem to be remarkably weak. From Figure 4, Ra has a small reduction with the increase of vc, but as fz and ae increase, Ra increases. Therefore, from the point of view of the influence of single factor on surface roughness, reducing fz and ae and increasing vc are helpful to reduce Ra.


### 3.4. Multiobjective Parameter Optimization Using NSGA-II

The response surface methodology is used to establish the mathematical model to analyze the influence of the parameters and to understand the parametric effect on process responses, but it is unable to solve the multiresponse problems. To avoid this limitation, multiobjective parameter optimization is necessary. In this study, NSGA-II is used for evaluation of optimal parametric combination. The NSGA-II is an improved approach of genetic algorithm (GA) for multiobjective optimization of process responses. Pareto-optimal solutions are obtained, and they are a set of nondominated solutions having high crowding distance.Unreasonable milling parameters lead to large milling force, poor surface quality, and low machining efficiency. Therefore, it is necessary to select reasonable milling parameters for the purpose of lowFt and Ra and high MRR. Material removal rate MRR, milling force Ft, and surface roughness Ra are conflicting, so the optimization of one target will cause other targets to become worse. Therefore, in order to minimize Ft and Ra as well as maximize MRR, NSGA-II is used for multiobjective parameter optimization to obtain the optimal fitness value of the objective function.NSGA-II has been run in MATLAB environment. The initial parameter setting for this algorithm is population size of 200 and evolution algebra of 200 generations. The obtained Pareto-optimal solution set is shown in Figure5(a). The X-axis, Y-axis, and Z-axis represent Ft, Ra, and MRR, respectively. It can be seen from Figure 5 that in Pareto-optimal solution set, when one response changes, other responses also change. The 30 solutions in Pareto-optimal solution set and the milling parameter corresponding to each solution are listed in Table 7. It is worth noting that because of the heuristic algorithm used, the results of each run will be slightly different. According to the requirements, the appropriate combination of milling parameters can be selected.Figure 5
Pareto-optimal solution set. (a) Pareto-optimal surface. (b) The distribution of 30 solutions.
(a)(b)Table 7
Results of NSGA-II (only first 30 solutions were taken).
Number of testsProcess parameterMilling forceFt (N)Surface roughnessRa (μm)Material removal rate MRR (mm3/min)vc (m/min)fz (mm/z)ap (mm)ae (mm)125.120.065.002.00455.320.3521919217.250.031.000.5059.100.26432325.120.025.000.50123.860.147188416.630.021.000.5061.790.25821525.120.065.002.00455.320.3521919625.120.065.001.96451.130.3521882725.120.065.001.18328.630.3051101825.120.065.001.15315.810.2951034925.120.065.000.56190.920.1985051025.110.055.000.60196.720.2035281124.490.061.000.73121.850.2961351225.120.035.000.50126.050.1482091325.120.055.000.65206.820.2125661425.120.064.971.02297.790.2839411525.120.035.000.50129.290.1492451625.110.054.992.00430.780.33317411724.480.041.150.5786.280.251801825.090.065.001.52392.490.34114571925.120.065.000.95278.760.2708632025.120.055.000.64204.380.2105572125.120.045.000.50136.580.1532942225.120.065.000.81256.170.2537642325.120.065.000.93275.790.2678502425.120.065.000.96281.360.2728752525.120.065.000.53181.750.1904722625.120.065.000.94283.350.2748842725.120.065.000.75233.950.2346732825.120.065.001.35349.010.31412042924.600.061.000.5695.740.2751033025.090.065.001.49381.390.3341390Figure5(b) shows the distribution of 30 solutions, which are evenly distributed and representative. According to the actual conditions, the suitable combination of milling parameters can be selected to obtain better results.


### 3.5. Confirmation

The results obtained can be compared with the results under the initial parameters of the experiment or the center point of RSM, as shown in Table8. The comparison results show that solutions in Pareto-optimal solution set have lower Ft and Ra and higher MRR than the center point of RSM.Table 8
Comprehensive optimized result.
NumberFt (N)Ra (μm)MRR (mm3/min)9190.920.19850519278.760.270863Experimental center287.740.326360


## 3.1. Results and Regression Model

Specific experimental scheme and results are shown in Table4.The mathematical relation between the control parameters and the output responses is developed using nonlinear second-order regression equation (1). Finally, the regression model describes the process parameters and milling force; the process parameters and surface roughness are given in Table 5.Table 5
Regression models andR2 values.
Regression modelsR2Ft=−54.3−1.18vc−2429fz+104.2ap+129.0ae−18.9vcfz−0.209vcap−0.673vcae+265fzap+1209fzae+22.76apae+0.066vc2+32117fz2−16.98ap2−47.6ae20.9940Ra=0.227−0.0072vc+1.89fz−0.0203ap+0.3075ae−0.198vcfz−0.000955vcap−0.00656vcae+0.209fzap+0.783fzae+0.02275apae+0.000355vc2+35fz2+0.00037ap2−0.0791ae20.9719The model prediction ability is commonly measured by the value of termR2. R2 value greater than 0.9 indicates that all the predicted values obtained by the regression model are within reliable interval. R2 values of regression models of Ft and Ra are 0.9940 and 0.9719, respectively. Figure 2 shows the correlation of the experimental milling forces and the predicted values obtained from the regression model, in which the position of the points is determined by the experimental value and predicted value of the same process parameter combination. The closeness of these points with the linear curves (y = x) indicates how compatible the predicted values are with the actual values. It can be seen that the distribution of points tends to be linear (y = x), suggesting that the results have no large deviation. Therefore, it is sufficient to say that the milling force and surface roughness regression model established by the response surface method are effective.Figure 2
Correlation of predicted values versus experimental values: (a)Ft; (b) Ra.
(a)(b)


## 3.2. Significance Test of Process Parameters

ANOVA is used to judge the significance of each factor to the responses. ANOVA results are listed in Table6. P value of P<0.05 (5% importance value) indicates a statistically significant effect of the parameters or interaction on the response value. F value of the parameters or interaction indicates the contribution of the source to the response value, and the greater the F value, the greater the contribution of the factor to the response value.Table 6
The ANOVA forFt and Ra.
SourceFtRaFPRemarksFPRemarksvc4.530.0503205.58<0.0001✓fz233.46<0.0001✓83.42<0.0001✓ap748.38<0.0001✓0.0660.8005ae974.55<0.0001✓131.3<0.0001✓vcfz0.670.425217.450.0008✓vcap0.820.37994.060.0622vcae1.190.29226.880.0001✓fzap13.350.0023✓1.980.18fzae39.06<0.0001✓3.890.0672apae138.48<0.0001✓32.84<0.0001✓vc20.130.72420.890.3594fz23.180.0950.890.3594ap288.8<0.0001✓0.010.9211ae213.810.0021✓9.050.0088✓Accordingly, forFt, the most effective parameter is seen to be ae, followed by ap and fz. vc has no significant effect on Ft. For Ra, the most effective parameter is seen to be vc, followed by ae and fz. ap has no significant effect on Ra. Moreover, the quadratic effect of ap2 as well as the interaction of ap and ae has the most influential contribution to Ft. And the quadratic effect of ae2 as well as the interaction of ap and ae has the most influential contribution to Ra.In the given ANOVA tables, besides the remarked effective parameters, the other parameters also have some effects that can be found from theirF value. But these effects are relatively weak and can be neglected in analysis.


## 3.3. Response Surfaces and Analysis

According to the regression model in Table5, taking two process parameters as variables and keeping the other two process parameters at 0 level, we can obtain the three-dimensional (3D) response surface in which the cutting force varies with these two process parameters. Figures 3 and 4 present the 3D response surfaces on milling force and surface roughness by variable factors, respectively. Through the 3D response surfaces, the influence of each process parameter and its interaction on milling force and surface roughness can be seen intuitively.Figure 3
3D response surfaces onFt: (a) vc − fz; (b) vc − ap; (c) vc − ae; (d) fz − ap; (e) fz − ae; (f) ap − ae.
(a)(b)(c)(d)(e)(f)Figure 4
3D response surfaces onRa: (a) vc − fz; (b) vc − ap; (c) vc − ae; (d) fz − ap; (e) fz − ae; (f) ap − ae.
(a)(b)(c)(d)(e)(f)The effects ofvc on Ft seem to be remarkably weak, as shown in Figures 3(a)–3(c). Ft has a small reduction with the increase of vc. As the milling speed increases, the milling temperature increases and the friction coefficient decreases. Meanwhile, the shear angle increases and the shear area decreases. So, the decreasing Ft, as a result of decreased friction and shear area, is an anticipated outcome.From Figure3, the milling force increases with the increment of fz, ap, and ae. From the characteristics of circumferential milling process, it can be seen that the cutting thickness per tooth increases with the increase of feed per tooth and the milling area increases with the increase of axial depth of cut and radial depth of cut. The generally accepted theory for calculating milling forces is that milling forces are positively correlated to the fz, ap, and ae. Therefore, from the point of view of the influence of single factor on milling force, reducing fz, ap, and ae is helpful to reduce milling forces.From Figures4(b), 4(d), and 4(f), the effects of ap on Ra seem to be remarkably weak. From Figure 4, Ra has a small reduction with the increase of vc, but as fz and ae increase, Ra increases. Therefore, from the point of view of the influence of single factor on surface roughness, reducing fz and ae and increasing vc are helpful to reduce Ra.


## 3.4. Multiobjective Parameter Optimization Using NSGA-II

The response surface methodology is used to establish the mathematical model to analyze the influence of the parameters and to understand the parametric effect on process responses, but it is unable to solve the multiresponse problems. To avoid this limitation, multiobjective parameter optimization is necessary. In this study, NSGA-II is used for evaluation of optimal parametric combination. The NSGA-II is an improved approach of genetic algorithm (GA) for multiobjective optimization of process responses. Pareto-optimal solutions are obtained, and they are a set of nondominated solutions having high crowding distance.Unreasonable milling parameters lead to large milling force, poor surface quality, and low machining efficiency. Therefore, it is necessary to select reasonable milling parameters for the purpose of lowFt and Ra and high MRR. Material removal rate MRR, milling force Ft, and surface roughness Ra are conflicting, so the optimization of one target will cause other targets to become worse. Therefore, in order to minimize Ft and Ra as well as maximize MRR, NSGA-II is used for multiobjective parameter optimization to obtain the optimal fitness value of the objective function.NSGA-II has been run in MATLAB environment. The initial parameter setting for this algorithm is population size of 200 and evolution algebra of 200 generations. The obtained Pareto-optimal solution set is shown in Figure5(a). The X-axis, Y-axis, and Z-axis represent Ft, Ra, and MRR, respectively. It can be seen from Figure 5 that in Pareto-optimal solution set, when one response changes, other responses also change. The 30 solutions in Pareto-optimal solution set and the milling parameter corresponding to each solution are listed in Table 7. It is worth noting that because of the heuristic algorithm used, the results of each run will be slightly different. According to the requirements, the appropriate combination of milling parameters can be selected.Figure 5
Pareto-optimal solution set. (a) Pareto-optimal surface. (b) The distribution of 30 solutions.
(a)(b)Table 7
Results of NSGA-II (only first 30 solutions were taken).
Number of testsProcess parameterMilling forceFt (N)Surface roughnessRa (μm)Material removal rate MRR (mm3/min)vc (m/min)fz (mm/z)ap (mm)ae (mm)125.120.065.002.00455.320.3521919217.250.031.000.5059.100.26432325.120.025.000.50123.860.147188416.630.021.000.5061.790.25821525.120.065.002.00455.320.3521919625.120.065.001.96451.130.3521882725.120.065.001.18328.630.3051101825.120.065.001.15315.810.2951034925.120.065.000.56190.920.1985051025.110.055.000.60196.720.2035281124.490.061.000.73121.850.2961351225.120.035.000.50126.050.1482091325.120.055.000.65206.820.2125661425.120.064.971.02297.790.2839411525.120.035.000.50129.290.1492451625.110.054.992.00430.780.33317411724.480.041.150.5786.280.251801825.090.065.001.52392.490.34114571925.120.065.000.95278.760.2708632025.120.055.000.64204.380.2105572125.120.045.000.50136.580.1532942225.120.065.000.81256.170.2537642325.120.065.000.93275.790.2678502425.120.065.000.96281.360.2728752525.120.065.000.53181.750.1904722625.120.065.000.94283.350.2748842725.120.065.000.75233.950.2346732825.120.065.001.35349.010.31412042924.600.061.000.5695.740.2751033025.090.065.001.49381.390.3341390Figure5(b) shows the distribution of 30 solutions, which are evenly distributed and representative. According to the actual conditions, the suitable combination of milling parameters can be selected to obtain better results.


## 3.5. Confirmation

The results obtained can be compared with the results under the initial parameters of the experiment or the center point of RSM, as shown in Table8. The comparison results show that solutions in Pareto-optimal solution set have lower Ft and Ra and higher MRR than the center point of RSM.Table 8
Comprehensive optimized result.
NumberFt (N)Ra (μm)MRR (mm3/min)9190.920.19850519278.760.270863Experimental center287.740.326360


## 4. Conclusions

The present paper highlights the application of response surface methodology central composite design to investigate the parametric effects on milling responses such as milling force and surface roughness of AF1410 steel during peripheral milling. The responses in milling operation such as milling force and surface roughness are compared with developed regression equation to know the validity of the mathematical model.R2 of regression models of milling force and surface roughness is 0.9940 and 0.9719, respectively. It indicates that all the predicted values obtained by the regression model are within reliable interval and suggests that the predicted model can be taken into consideration for further analysis. Unreasonable milling parameters lead to large milling force, poor surface quality, and low machining efficiency. Therefore, there is a requirement of optimization of process parameters to achieve the milling objectives of low milling force Ft and surface roughness Ra and high material removal rate MRR. The NSGA-II has been applied to obtain a set of optimal combination of parameters from the Pareto-optimal solution set to enhance the machining conditions.



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*Source: 8796738-2020-07-27.xml*