Microsoft Word - ETASR_V13_N2_pp10447-10452 Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10447-10452 10447 www.etasr.com Nguyen et al.: Multiple Response Prediction and Optimization in Thin-Walled Milling of 6061 … Multiple Response Prediction and Optimization in Thin-Walled Milling of 6061 Aluminum Alloy Van Que Nguyen Faculty of Mechanical Engineering, Hanoi University of Industry, Vietnam nguyenvanque@haui.edu.vn Hoang Tien Dung Faculty of Mechanical Engineering, Hanoi University of Industry, Vietnam tiendung@haui.edu.vn Van Thien Nguyen Personnel and Administrative Department, Hanoi University of Industry, Vietnam nguyenvanthien@haui.edu.vn Van Dong Pham Department of Science and Technology, Hanoi University of Industry, Vietnam nguyenvanthien@haui.edu.vn Van Canh Nguyen Faculty of Mechanical Engineering, Hanoi University of Industry, Vietnam nguyenvancanh@haui.edu.vn (corresponding author) Received: 10 January 2023 | Revised: 4 February 2023 | Accepted: 15 February 2023 ABSTRACT In this study, the multi-objective optimization method for thin-wall milling of 6061 aluminum alloy is addressed. The technological parameters including the cutting speed Vc, the feed of tooth fz, and the width of cut ar are considered input variables, while the manufacturing responses are surface roughness Ra, production rate MRR, and flatness deviation FL. The goal is to find the optimum cutting parameters to minimize Ra and FL and maximize MRR, at the same time. To solve this problem, the desirability function approach was used based on Taguchi orthogonal array. Twenty-seven experiments were conducted and the measured data were collected. The mathematical regression models for responses Ra, MRR, and FL were then generated and evaluated by using the analysis of variance method. Then, the multiple objective optimization problems were solved by using the desirability function approach. The optimum cutting parameters set are Vc=120m/min, fz=0.06mm, and ar=0.13131mm, corresponding to Ra=0.1613µm, MRR=17197.45cm 3 /min, and FL=0.0995mm. Keywords-thin-walled milling; multiple objective optimization; desirable function approach; Taguchi method; 6061 aluminum alloy I. INTRODUCTION The 6061 alloy is an important product line in aluminum manufactured products [1]. Aluminum and its alloys rank second (after steel) in use as structural metals [2], due to properties that make them suitable for many different uses [3]. Some of the important properties of 6061 alloy are its light weight, high strength, good chemical corrosion resistance, and good weldability [4]. Therefore, 6061 alloy is often used in the transportation industry (e.g. in auto parts, motorcycles, cycle frames, and motorcycle frames) and especially in the marine or aerospace industry [5]. The development of the aviation Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10447-10452 10448 www.etasr.com Nguyen et al.: Multiple Response Prediction and Optimization in Thin-Walled Milling of 6061 … industry has led to an increasing demand for aluminum alloy machining, in which the milling of thin-walled parts plays a particularly important role [6]. However, the manufacturing of thin-walled parts is complicated by the possibility of deformation during the machining process [7]. Thin-walled products are often difficult to cut due to the complex dynamics involved. During the cutting process, the cutting dynamics for the products varies however it is invariant for the machine tool [8]. On another hand, permanent deformation of the structure can occur and this can cause a proportion of rejected products [9]. In the demand of the growing global market for aluminum alloy thin-walled products, there are several studies focused on optimizing the structure to improve the surface roughness, the load capacity, and the durability of the thin-walled components by reducing deformation and vibration during the cutting process [7]. Μany studies have been carried out to improve the economic and technical efficiency of thin-walled processing. Authors in [10] developed an analytical approach to investigate the dynamic chip thickness variation in the thin-walled milling process. A general model of the removal volume is calculated by considering the individual axial depth of cut, the radial depth of cut, and the circumferential cross-section of the tool radius contact for each tool step performed. Authors in [6] presented a technique to improve the surface quality and production rate in the thin-walled milling process. The results show that double-side milling leads to reduce about 50% in cutting time and a decline in the surface roughness and flatness deviation of the milling products, simultaneously. The quality of thin-walled products when machined can also be improved by selecting and using the right jigs and fixtures [11]. Finding suitable cutting parameters can also reduce vibration, thereby reducing deformation during milling. This can be solved through experimentation [12, 13], or mathematical modelling [14]. Authors in [8] present a methodology of performing the optimization of the entire cutting process for thin-walled parts based on the relatively changing kinematics of the machining system. According to the comparison between the dynamics of the machine tool and the variable thickness part, the critical thickness is investigated by an iterative algorithm. This method can be used for many other machining processes. There are many other studies on machining thin-walled parts in general, and aluminum alloys in particular. These studies can be applied to improve the quality of processed products in practice. However, due to the increasing competitive pressure from the global market, the manufacturers not only have to improve the quality of processing but at the same time have to increase machining productivity and tool life. Those are scientific multi-objective optimization problems and Multiple Criteria Decision-Making (MCDM) methods such as the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and Multi-Objective Optimization on the basis of Ratio Analysis (MOORA) have been introduced to face them [15-19]. They are often applied due to their simplicity. However, these methods have a common disadvantage, which is the optimal value set is one of the experimental values. This means that these techniques select one of the data sets that have been used, and in many cases, they are not the best [18-20]. With the development of computers, many new algorithms have been researched and applied, e.g. ANFIS [21], Desirability Function Approach (DFA) [22], etc. Many publications have demonstrated the effectiveness of these methods in comparison with MCDM. In this study, DFA and Minitab computed software were applied to solve the multi- objective optimization problem at hand. The research aims to find the optimal cutting parameters set to simultaneously maximize the machining productivity MRR, and minimize the roughness Ra and flatness deviation FL. A. MATERIALS AND METHODS B. 6061 Aluminum Alloy As mentioned above, 6061 Aluminum Alloy was selected because it is largely used. All the specimen workpieces were milled with dimensions of 100×50×10mm 3 . The chemical composition and mechanical properties of the workpieces are shown in Tables I and II [23]. The experiments were conducted on a DMU50 CNC Machine. To perform thin-walled milling operations, a 3-flute square namely YG ALU - CUTTER E5D70100 (15329040K) was used (Figure 1). The Taguchi orthogonal array was applied to reduce the number of experiments but still ensure reliability in the predictive analysis, with the number of input variables being 3, the number of levels for each variable being 3, and the number of experiments to be performed being 27. The values of the input variables corresponding to the levels are depicted in Table III. The range of the cutting parameters is chosen based on the cutting tool manufacturer’s recommendations. TABLE I. CHEMICAL COMPOSITION OF 6061 ALLOY Al (%) Mg (%) Si (%) Cu (%) Cr (%) Others (%) 97.9 1 0.60 0.28 0.20 0.02 TABLE II. THE MECHANICAL PROPERTIES OF 6061 ALLOY Tensile strength 310MPa Yield strength 276MPa Shear strength 207MPa Fatigue strength 96.5MPa Elastic modulus 68.9GPa Poisson's ratio 0.33 Elongation 12-17% Hardness 95 HB TABLE III. INPUT VARIABLE LEVELS Parameters Symbol Unit Level -1 0 1 Cutting speed Vc m/min 120 150 180 Feed rate fz mm/tooth 0.04 0.05 0.06 Width of cut ar mm 0.8 1.0 1.2 C. Experimental data acquisition The experimental set up is shown in Figure 2. In this work, 3 thin-walled cutting responses, including the surface roughness Ra, material removal rate MRR, and flatness deviation FL are optimized simultaneously by applying the Desirable Function Approach (DFA). Based on the EN ISO 4287 standard, surface roughness Ra is calculated by: Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10447-10452 10449 www.etasr.com Nguyen et al.: Multiple Response Prediction and Optimization in Thin-Walled Milling of 6061 … ��� = ���� ��� ���� ���� ��� � (1) ��� = ���� ��� ���� ���� ��� � (2) �� = ��� ���� (3) where Rax is the arithmetical mean roughness in the x-direction and Ray is the mean roughness depth in the y-direction. Fig. 1. The experimental setup. Fig. 2. a1: Negative local flatness deviation, a2: Positive local flatness deviation, 1: least squares reference plane (STN P CEN ISO/TS 12781-1: 2008). (a) (b) Fig. 3. Measurement systems. (a) Renishaw Equator 300 CMM - High- Speed Comparative Gauge System, (b) Non-contact flatness deviation measurement system. TABLE IV. EXPERIMENTAL RESULTS Run Vc m/min fz mm/ ar mm Ra µm MRR mm 3 /min FL mm 1 120 0.04 0.8 0.228 8025.48 -0.031 2 120 0.05 1 0.128 14331.21 -0.060 3 120 0.06 1.2 0.152 20636.94 -0.044 4 150 0.04 0.8 0.294 10031.85 0.100 5 150 0.05 1 0.274 17914.01 0.063 6 150 0.06 1.2 0.345 25796.18 0.131 7 180 0.04 0.8 0.157 11369.43 -0.015 8 180 0.05 1 0.170 20302.55 -0.045 9 180 0.06 1.2 0.271 29235.67 0.039 10 180 0.04 1 0.150 16242.04 0.050 11 180 0.05 1.2 0.205 24363.06 0.085 12 180 0.06 0.8 0.206 17054.14 0.029 13 120 0.04 1 0.190 11464.97 0.033 14 120 0.05 1.2 0.172 17197.45 0.048 15 120 0.06 0.8 0.170 12038.22 -0.023 16 150 0.04 1 0.275 14331.21 0.085 17 150 0.05 1.2 0.300 21496.82 0.192 18 150 0.06 0.8 0.300 15047.77 0.130 19 150 0.04 1.2 0.292 17197.45 0.368 20 150 0.05 0.8 0.279 12539.81 0.058 21 150 0.06 1 0.309 21496.82 0.055 22 180 0.04 1.2 0.175 19490.45 0.253 23 180 0.05 0.8 0.163 14211.78 -0.050 24 180 0.06 1 0.227 24363.06 -0.046 25 120 0.04 1.2 0.196 13757.96 0.234 26 120 0.05 0.8 0.181 10031.85 -0.084 27 120 0.06 1 0.161 17197.45 -0.099 In this experiment, the surface roughness value of each experiment was measured 3 times on a Renishaw Equator 300 CMM - High-Speed Comparative Gauge System (Figure 3) according to the EN ISO 4287 standard. The flatness deviation (FL, mm) is measured using a non-contact measurement system (Figure 3). According to STN P CEN ISO/TS 12781-2: 2008 standard, the flatness zone was divided into negative and positive (Figure 2) local zones based on the least squares reference plane, which is a plane such that the sum of the squares of the local flatness deviations is minimum. The measured results are summarized in Table IV. The Material Removal Rate-MRR (mm 3 /min) of each experiment is calculated by: ��� = �� × �� × � × � × �� (4) where ap is the depth of cut (mm). In this experimental work, ap=10mm for all runs. ar is the width of cut (mm), N is the number of cut flutes (N=3), S is the spindle speed (rpm), and fz is the feed of tooth (mm/tooth). The matrix of the experiment design with the input factors and the response data is presented in Table IV. These data were utilized to develop the regression models for Ra, MRR, and FL. D. The Optimization Problem The machining parameters, i.e. cutting speed Vc, feed rate fz, and width of cut ar, and their corresponding levels are listed in Table III. The target of this research is to decrease the flatness deviation FL and improve the MRR concerning the predefined Ra. Consequently, the optimizing issue can be described as (5): Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10447-10452 10450 www.etasr.com Nguyen et al.: Multiple Response Prediction and Optimization in Thin-Walled Milling of 6061 … Find X={Vc, fz, ar} to minimize {Ra; FL}, and maximize MRR subjected to 120 ≤ Vc ≤ 180 (m/min); 0.04 ≤ fz ≤0.06 (mm/tooth) and 0.8 ≤ ar ≤ 1.2 (mm) (5) To solve this multi-object problem, the DFA was adopted. The desirability package contains S3 classes to optimize multiple variables simultaneously using the DFA of Harrington [24-26] (1965) with the functions described in [24, 25]. Basically, the method is to translate the functions to a common scale ([0, 1]), combine them using the geometric mean and optimize the overall index. For each function R, an individual "desirability" function is constructed to be high when fr(x) is at the desired level (such as maximum, minimum, or target) and low when the fr(x) is at an unwanted level value. Authors in [27] proposed three forms of these functions, corresponding to the type of optimization goal. To maximize fr(x), ����� , ������ are obtained for maximization and minimization purposes, while ��!��"�! represents for the best solution. ����� = # 0 if �� '() < +,-.'�)/01/0 23 if + ≤ �� '() ≤ 51 if �� '() > 5 (6) ����� = # 0 if �� '() > 5,-.'�)/10/1 23 if + ≤ �� '() ≤ 51 if �� '() < + (7) ��!��"�! = ⎩⎪⎨ ⎪⎧ ,-.'�)/0!?,-.'�)/1!? ≤ �� '() ≤ 50 otherwise (8) II. RESULTS AND DISCUSSION A. Regression models The regression models for Ra, MRR, and FL were generated using Minitab Software. Equations (9)-(11) show the fully developed regression models. �� = −1.609 + 0.04550NO − 38.20�� − 1.066�� −0.000188NO� + 173.9��� + 0.2767��� + 0.1307NO �� +0.002964NO . �� + 2.53�� �� (9) MRR = 16932 − 115.4NO − 338641�� − 17516�� −0.0000NO� + 0.0000��� + 0.0000��� + 2309NO �� +119.43NO . �� + 340318�� �� (10) VW = −2.390 + 0.05237NO − 33.26�� − 1.267�� −0.000188NO� + 465.7��� + 1.470��� + 0.0490NO �� +0.00407NO . �� − 26.42�� �� (11) To assess the adequacy of these models, analysis of variance (ANOVA) was adopted. The ANOVA was conducted with 95% of confidence and 5% significance. The ANOVA results for the predictive models are presented in Tables V-VII. The coefficients of mathematical regression models, including "R 2 ", "adjusted R 2 ," and "predicted R 2 ," reveal the accuracy of the developed models. In this work, the values of "R 2 ", "adjusted R 2 ," and "predicted R 2 ," for Ra, MRR, and FL the are fluctuated in the range of [96.66%, 99.93%], [94.89%, 99.89%], and [89.78%, 99.76%] mean a good fitting between the experimental and the predicted values. Hence, it is concluded that the developed models of Ra, MRR, and FL can be used for predicting the optimal process parameters. TABLE V. ANOVA FOR THE PREDICTIVE MODELS OF Ra Term DF Adj SS Adj MS F-Value P-Value Regression 9 0.102879 0.011431 54.64 0 Vc 1 0.039154 0.039154 187.14 0 fz 1 0.006102 0.006102 29.16 0 ar 1 0.003528 0.003528 16.86 0.001 Vc*Vc 1 0.079044 0.079044 377.8 0 fz*fz 1 0.001814 0.001814 8.67 0.009 ar*ar 1 0.001452 0.001452 6.94 0.017 Vc*fz 1 0.012573 0.012573 60.09 0 Vc*ar 1 0.004044 0.004044 19.33 0 fz*ar 1 0.000413 0.000413 1.97 0.178 Error 17 0.003557 0.000209 Total 26 0.106436 "R 2 "=96.66%, "Adjusted R 2 "=94.89% and "predicted R 2 "=89.78% TABLE VI. ANOVA FOR THE PREDICTIVE MODELS OF MRR Term DF Adj SS Adj MS F-Value P-Value Regression 9 728005304 80889478 2553.25 0 Vc 1 199266 199266 6.29 0.023 fz 1 720212 720212 22.73 0 ar 1 1209228 1209228 38.17 0 Vc*Vc 1 1999162 1999162 63.1 0 fz*fz 1 0 0 0 1 ar*ar 1 4602114 4602114 145.26 0 Vc*fz 1 3998324 3998324 126.21 0 Vc*ar 1 6685664 6685664 211.03 0 fz*ar 1 9204227 9204227 290.53 0 Error 17 538577 31681 Total 26 728543881 "R 2 "=99.93%, "Adjusted R 2 "=99.89% and "predicted R 2 "=99.76% TABLE VII. ANOVA FOR THE PREDICTIVE MODELS OF FL Term DF Adj SS Adj MS F-Value P-Value Regression 9 0.315328 0.035036 97.42 0 Vc 1 0.058999 0.058999 164.04 0 fz 1 0.002633 0.002633 7.32 0.015 ar 1 0.006217 0.006217 17.28 0.001 Vc*Vc 1 0.08127 0.08127 225.96 0 fz*fz 1 0.013011 0.013011 36.17 0 ar*ar 1 0.03372 0.03372 93.75 0 Vc*fz 1 0.001546 0.001546 4.3 0.054 Vc*ar 1 0.000111 0.000111 0.31 0.585 fz*ar 1 0.054928 0.054928 152.72 0 Error 17 0.006114 0.00036 Total 26 0.321442 "R 2 "= 98.10%, "Adjusted R 2 "=97.09% and "predicted R 2 "=96.09% B. Multiple Objective Optimization results As mentioned above, the DFA was adopted for solving the multiple objective problem (Figure 4). The Composite Desire Values (D) corresponding to 27 experiments were computed using the Minitab 19 software with the constrain from (5). The results are shown in Table VIII. Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10447-10452 10451 www.etasr.com Nguyen et al.: Multiple Response Prediction and Optimization in Thin-Walled Milling of 6061 … (a) Hold value: ar=1 Hold value: fz=0.05 Hold value: Vc=150 (b) Hold value: ar=1 Hold value: fz=0.05 Hold value: Vc=150 (c) Hold value: ar=1 Hold value: fz=0.05 Hold value: Vc=150 Fig. 4. Surface plot of (a) FL, (b) Ra, (c) MRR vs Vc, fz, ar. TABLE VIII. COMPOSITE DESIRABILITY VALUE (D) Solution Vc fz ar FL fit MRR fit Ra Fit D 1 120 0.060 1.131 -0.07 19829.00 0.145 0.769 2 120 0.060 1.180 -0.04 20596.40 0.149 0.763 3 120 0.060 1.199 -0.03 20866.70 0.151 0.758 4 120 0.060 1.200 -0.03 20879.10 0.151 0.757 5 180 0.058 1.052 -0.04 24881.10 0.223 0.718 6 180 0.060 1.034 -0.04 25165.70 0.233 0.699 7 180 0.060 1.012 -0.04 24533.80 0.230 0.698 8 180 0.060 1.137 0.00 27867.10 0.255 0.662 The higher the value of D, the more optimal the experiment is. In this study, the optimal parameter set Vc = 120m/min, fz = 0.06mm, ar = 1.13131mm correspond to Ra = 0.144601µm, MRR = 19829cm 3 /min, and FL = -0.00699460mm. Comparing the optimization results with the resurged results shown in Table I, it is easy to see that the optimization results are quite close to the experiment number 27. However, the difference is that the predicted ar value is larger than the selected ar value, at 1mm and 1.131mm, respectively. This increase in the width of the cut led to an increase in production rate by about 15.30%, from 17197.45 to 19829cm 3 /min. At the same time, the surface roughness value Ra decreased by 13.10%, from 0.1613 to 0.1446µm and the FL also decreased by -0.07mm, a decrease of 29.65%. The results of this study show the advantages of DFA in comparison with DCDM. The disadvantage of DCDM is that the optimal parameter set is calculated, ranked, and selected from one of the experimental runs, in this case, experiment number 27. With the DFA method, the optimal parameters do not necessarily coincide with the selected parameters. The comparison results are clearly depicted in Table IX. TABLE IX. OPTIMIZATION RESULT COMPARISON Cutting parameters Responses Vc (m/min) fz (mm) ar (mm) Ra (µm) MRR (cm3/min) FL (mm) Actual value 120 0.06 1 0.1613 17197.45 -0.0995 Predicted value 120 0.060 1.131 0.145 19829.00 -0.07 Comparison 13.10% 15.30% 29.65% III. CONCLUSION Due to the increasing competitive pressure from the global market, the need to maintain or increase product quality while simultaneously increasing productivity is important. This is a multi-objective optimization problem. In this article, the multiple objective optimization issue in thin-walled milling of 6061 aluminum alloy for reducing flatness deviation FL and surface roughness Ra while improving production rate MMR simultaneously, has been addressed. Predictive mathematical regression models of the three responses have been developed to model the highly non-linear relations between the cutting parameters (i.e. Vc, fz, and ar) and the machining responses. The Desirability Function Approach (DFA) was employed to Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10447-10452 10452 www.etasr.com Nguyen et al.: Multiple Response Prediction and Optimization in Thin-Walled Milling of 6061 … generate the optimum parameters. The main results of this work can be concluded, as follows: The "R 2 ", "adjust-R 2 " and "predicted-R 2 " of Ra, MRR, and FL fluctuated around 90-99%, illustrating the good relationship between cutting parameters and response. Hence, these mathematical regression models could be applied in the actual manufacturing process to predict the cutting parameters set corresponding to the desired response. The obtained optimal cutting parameters set of thin-walled milling of 6061 aluminum alloy processes is (Vc=120m/min, fz=0.06mm, and ar=1.13434mm), corresponding to the Ra, MRR, and FL values of 0.14269µm, 19614.6mm 3 /min, and -0.0653mm, respectively. The findings in this research work can contribute to a broader understanding of aluminum alloy thin-walled milling and can be extended to research with other materials and machining processes. In future works, other cutting parameters such as tool nose radius, tool coaching material, lubrication method, number of inserts, number of flutes, and other responses including cutting force, cutting variation, tool wear, and tool life will be taken into consideration. ACKNOWLEDGMENT This research is supported by the Hanoi University of Industry (HaUI). REFERENCES [1] D. Carou and J. P. Davis, Eds., Machining of Light Alloys: Aluminum, Titanium, and Magnesium, 1st ed. Boca Raton: CRC Press, 2018. [2] J. R. 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