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## Application of Central Composite Design for Opt...

### By: Yanuar Burhanuddin

As of: Sep 22, 2020 7:24:35 AM
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Application of Central Composite Design for Optimization Machining Parameters When Machine Magnesium AZ31 Ahmad Yasir Md Said1, Gusri Akhyar Ibrahim2, Arinal Hamni3, Rabiah Suryaningsih4, Yanuar
Burhanuddin5 1University
Kuala Lumpur – Malaysia France Institute, Bandar Baru Bangi, Malaysia 2,
3, 4, 5Mechanical Engineering Department, University of Lampung, Indonesia Abstract:
Magnesium AZ31 are widely used for industrial manufacturing such as manufacturing aircraft components, automotive, biomaterials and sports. The interests of manufacturing industries for machining Magnesium AZ31 are to obtain high accuracy, high precision and high tool life. The purpose of this experiment is to achieve optimum cutting parameter for tool life and quality of surface finish. A mathematical model for tool life can be computed from this experiment. Magnesium alloy AZ31 as work piece material consist of 3% of aluminium and 1% of zinc. The parameters used for experimental trials were cutting speed (v) of 22, 32 and 42 m/min, depth of cut (d) of 1, 2, and 3 mm and feed rate (f ) of 0.15, 0.20, and 0.25 mm/rev. Minitab software was used to analyze the data obtained. The maximum actual tool life was 96.7 minutes or longer than 9.36% from the Central Composite Design prediction, which was 85.78 minutes. This maximum value achieved at cutting speed (v) of 42 mm/min, cutting depth (d) of 1 mm, and feed rate (f) of 0.15 mm/rev. Whereas the mathematical modeling for the magnesium AZ31 in the milling process is Y = 34.7 + 7.69v - 0.426f - 61.5d - 0.0688 v*v + 0.000539 f*f + 1.06 v*d + 0.0363 f*d. Keywords: RSM, CCD, magnesium AZ31, optimization, machining, parameters
1. Introduction close to +1 or there is a positive relationship between variable and response. The quality of magnesium AZ31 as the raw material for the machining process, especially the milling machining, can be 2. Literature Study seen by optimizing the value using Central Composite Design (CCD) Response Surface Method by calculating several Magnesium AZ31 is a mixture of magnesium with aluminum variables in milling process which influences the and zinc. Magnesium is a good nonferrous metal vibration optimization of the machinery itself such as cutting depth, damper so often used in structural and non-structural feeding and tool rate [1]. Some statistical and mathematical applications where weight of the material is preferred in the techniques are often used in order to gain an optimal transportation industry because the weight or absence of the conditions of a machining process, without requiring too vehicle structure affects the amount of fuel consumption [5]. much data. Among the frequently used methods is
the Central Composite Design (CCD) response surface method.
Simple Table 1: Physical properties of magnesium use by composing a mathematical model, the researcher can Physical Properties Magnesium Alloy detect the value of independent variables that have more Liquid Point, K 922 K influence to the response value to be optimal [2]. Compared Boiling Point,K 1380 K with other methods such as full factorial used to find Ionization Energy, I 738 KJ/mol interaction relations using 3 factors requires 27 data samples, Ionization Energy, II 1450 KJ/mol while using the Central Composite Design (CCD) only Mass Density (ρ) 1.74 g/cm3 requires 20 data samples, and with the same success rate of Atomic Radian 1.60 A research, the Central Composite Design (CCD) is more Heat Capacity 1.02 J/gK appropriate to be used in this research. Ionization Potential 7.646 Volt Conductivity of Heat 156 W/mK The number combination of factors is set up by the response Evaporation Entalpy 127.6 kJ/mol surface method of the Central Composite Design (CCD) on Forming Entalpy 8.95 kJ/mol the machining process for magnesium AZ31 with a total The magnesium manufacturing industry requires several sample of 23 + 6 + 6 = 20. So that the results obtained product characteristics that correspond to the properties of material cutting more subtle and precision [3]. The factors magnesium itself, which are lightweight, and are readily used in this research are tool rate (v), cutting depth (d) and given machining treatment. The machining process itself has feeding (f) using 3 stratified variables for each factor [4]. requirements that must be met to achieve the desired quality, Thiagarajan's research in 2012 shows that the Central the requirements to be considered include: Composite Design (CCD) method used to find out the 1) The machining is able to remove material from workpiece optimal value of drill machining in steel as a composite 2) Intended to create components matrix, takes 95% confidence level on all graphic results
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Accuracy property and also be adjustable if the range of response 4) Getting a precise form variables is completely unknown. In other words, the variety 5) Short cutting time of response variables that are allegedly the same for all points 6) Long life of cutting tool provided that the points have the same distance from the 7) High quality components center of the design (center runs). Three dimensional curves 8) Low production costs (Three dimensions response surface and contour plot) are 9) Environment support
used to test the true effect of experimental variables on the results
obtained. The coefficients in the empirical model are In the manufacturing industry the machining process is one estimated by using multi-regression analysis. The suitability way to produce the product in large quantities with a of the empirical model with the experimental data can be relatively short time. Many different types of machines are determined from the coefficient of determination (R2). To used, this means leading to different processes for each form test whether or not the empirical model produced is used of product. In the process of milling machining, the ANOVA (Analysis of Variance). In simple correlation workpiece is a type of material with certain mechanical analysis, it is possible to find that two variables are positively properties that are cut continuously by cutting tool to produce correlated, negative, or uncorrelated. the shape as required, therefore it
is necessary to adjust the material of the cutting tool. Because of this, the
age of the cutting tool itself becomes one of the most important machining requirements to be concerned to observe as it is directly related to other requirements such as low production costs and high component quality [6]. There are three main parameters that affect the cutting force, the increase of heat and integrity of the workpiece surface produced. The three
parameters are cutting velocity (v), feeding (f) and cutting depth (d). The cutting velocity is the speed around the workpiece
with the unit (m / min), feeding is the movement or distance of the cutting tool per unit of Figure 1: Central Composite Design in a box motion of the work piece with unit (mm / rev), the cutting depth is the thickness of the waste material in the feeding 3. Research Methodology direction by unit (mm ). Place of research conducted at the laboratory of Production The success of cutting with the milling machine is influenced
Department of Mechanical Engineering University of by the cutting ability of the
cutting tool and the machine. The Lampung for data retrieval. The test is at room temperature cutting capability involves cutting and feeding speeds. The condition varies from 27 °C to 35 °C. The cutting tools used cutting speed of the milling machine can be defined as the for this research are high speed steel. The material used in length of the waste that is cut off by one eye cutting the blade this research is magnesium AZ31.The first step is to set the in one minute. The cutting speed for each material is not the value of the increase the variables, with the table as follows: same. Generally the harder the material, the smaller the price of cutting speed and to the contrary. The cutting speed in Table 2: Variable value of central composite design milling process is determined based on the price of the
Cutting Speed (v) Feed rate (f) Depth of Cut (d) cutting speed according to the material and the
diameter of (mm/min) (mm/rev) (mm) the blade. 22 0.15 1 32 0,2 2 In response surface methodology, independent variables are 42 0,25 3 defined as X1, X2, ..., XK and assumed as continuous variables, whereas the response is defined as the dependent After that, do the machining using the AZ31 magnesium test variable Y which is a random variable [7]. The mathematical material. With the test format according to the coding table relationship describes the experimental response and the for the Central Composite Design method: unknown free variables, so the first step to do is to determine the approximate corresponding to the mathematical Table 3: Design parameters of central composite design connection. If a mathematical connection is already known, then it can be used to determine the most efficient operating Number Run Variable Coding Order Cutting Speed Feeding (f) Depth of Cut conditions. According to Garsperz (1992), usually the initial (v) (m/min) (mm/rev) (d) (mm) stage formulated models of polynomial regression with a low 1 5 -1 -1 -1 order, eg first order which is nothing but a linear regression 2 9 1 -1 -1 model, with the following equation: 3 16 -1 1 -1 4 8 1 1 -1 Y = β0 ¬+ β1x1 + β2x2 + … + β0x¬k + E 5 11 -1 -1 1 6 4 1 -1 1 7 14 -1 1 1 Using the central composite design (CCD), to have a better 8 6 1 1 1 quality than not using it, the design must have an orthogonal 9 15 -1 0 0
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10 18 1 0 0 11 3 0 -1 0 12 13 0 1 0 13 12 0 0 -1 14 20 0 0 1 15 2 0 0 0 16 1 0 0 0 17 7 0 0 0 18 17 0 0 0 19 19 0 0 0 20 10 0 0 0 The tool wear was measured progressively. Each experiment or run was stopped when the tool wear reached at the rejection criteria which is 0.2 mm. The tool then was replaced by the new tool and followed by new run. The tool life is obtained according to the machining time taken for the wear reached at this rejection criteria. All these data were analyzed using Minitab software in order to compute the mathematical model for the tool life. 4. Results and Discussions Table 4: Results obtained Run Order
Cutting Speed v, mm/ m Feeding f, mm/rev Depth of Cut d, mm
Tool life, minutes Tool Wear, Vb 1 32 0.2 2 13.38 0.2 2 32 0.2 2 13.38 0.2 3 32 0.15 2 32.6 0.2 4 42 0.15 3 37 0.2 5 22 0.15 1 40 0.2 6 42 0.25 3 4.4 0.2 7 32 0.2 2 17 0.2 8 42 0.25 1 4 0.2 9 42 0.15 1 96.7 0.2 10 32 0.2 2 13.38 0.2 11 22 0.15 3 64.2 0.2 12 32 0.2 1 50.1 0.2 13 32 0.25 2 6.48 0.2 14 22 0.25 3 11.4 0.2 15 22 0.2 2 6.34 0.2 16 22 0.25 1 9 0.2 17 32 0.2 2 13.38 0.2 18 42 0.2 2 5.45 0.2 19 32 0.2 2 13.38 0.2 20 32 0.2 3 15 0.2 Figure 2: Tool wear progression at variance of feedrate RO 5 is a combination of all lowest value variables (-1, -1, -1), RO 2 is a combination of all the middle value variables (0, 0, 0) and RO 6 is a combination of all highest value variables (1, 1, 1) . From tool life of low variable age of cutting tool for 40 minutes, to use of variable value of middle produce tool life for 13 minutes mean age of cutting tool decreased 67,5%, and from middle variable to low variable value with value 4 minute 24 second, decreased as much 68% . That is, the average decline in tool life value at each increase in the variation level is 67.75%. Cutting tool will experience wear and abration after being used for cutting, the greater the wear of cutting tool then the cutting tool condition will be more critical and the age of the cutting tool is getting shorter. If the cutting tool continues to be used then the wear of the cutting tool will be faster because the cutting edge will be damaged and lead to shorter cutting tool life, fatal damage should not occur on the cutting tool because a large cutting force will damage cutting tools, machine tools and workpieces and may endanger the operator as well as influence great on the geometry tolerance and surface quality of the product. The linear combination of cutting variables in Figure 2 shows a negative correlation, because the purpose of this study is the maximum cutting tool life. The negative correlation in question is when the cutting variable value is raised and used in the machining process of the frais, the value of the life of the cutting tool decreases or accelerates faster than if it uses a low cutting variable value [8]. Figure 3: Regression coefficient Figure 3 showed the result of the regression coefficient model in stage I. The value of the obtained coefficient shows the constant value of 9.08. So we get the following equation: Y = 9.08 + 1.49v – 23.52f – 6.60d, or T (tool life) = 9.08 + 1.49v – 23.52f – 6.60d According to the equation of linear regression line can be explained that: 1) The coefficient value v = 1.49 means that, if the velocity value (v) increases by one point, and the other independent variable remains, then the life of the tool will be added as the coefficient multiplier is 1.49. 2) The coefficient value f = -23.52 means that, if the value of the feeding motion (f) increases by one point, and the other independent variable is fixed, then the lifespan is reduced by 23.52% according to the coefficient multiplier value because the value of the coax is negative. 3) The coefficient value d = -6.60, means that if the depth of cut (d) value increases by one point, and the other independent variable is fixed, then the life of the tool (T) will decrease by 6.60 percent. Figure 4: Result of ANOVA (Analysis of variance) The hypothesis for this model is H0 = the effect of the variable value on the response. H1 = absence of influence of variable value to response. Possible data error (α) = 5% = 0.05 From the data above shows that the value of P-value of feeding motion variable (f) 0.000 and P-value of cutting depth (d) of 0.019 is smaller than when α = 0.05, meaning that the feeding motion and the depth of the cut
affect the wear of cutting tool. min. With the value of the
lack-of-fit test showing the result of 0 then the second order model can be accepted as the optimization model in the frais machining application. The using of mathematical modeling according to the predicted Y result is as follows : Y = 34.7 + 7.69 (42) - 0.426 (137) - 61.5 (1) - 0.0688 (422) + 0.000539 (1372 ) + 19.77 (12 ) - 0.00352 (42x137) - 1.074 (42x1) + 0.0363 (137x1) = 85.7887 minutes The prediction of tool life of the second order model results for 85.7887 minutes using the optimum point of each variable is v = 42 mm /
min, f = 0.15 mm / rev, and d = 1 mm,
while the actual test uses the combination of parameters similar to the optimum points of each variable yielded the lifetime of the length of 9.36% ie 96.7 minutes or 96 minutes 42 seconds. Figure 5: Normal probability plot At the 20 sample points used, it shows the normal residual distribution close to the red line. The farthest drift from the normality test chart above is run order 20 with residual percentage reaching 23.03%. Figure 7: Optimization value of magnesium AZ31 The plot optimization shows the optimum point of the recommended milling machine based on this research, after the result of the research data is tabulated on the minitab software obtained the result as Figure 7 above. The picture shows that the optimum point for milling machining in this research used the variable value of cutting speed of 42 or using the highest variable value, low feeding variable is 0.15 mm / rev and low cut depth variable is 1 mm. The optimum point is obtained from the data table (Graphic 4), is run order 9. Figure 6: Central Composite Design for second order A mathematical model as below is obtained: Figure 8: Plot contour T = 34.7 + 7.69 v - 0.426 f - 61.5 d -
0.0688 v*v + 0.000539 f*f + 19.77 d*d
- 0.00352 v*f - 1.074 v*d The green color is seen in all of the combining variable surface + 0.0363 f*d regions (f.v), (d.v), (d.f). The combined region shows that the area of maximum optimization is present in the feeding area of Modeling shows the value of Y prediction is smaller than
0.15 mm / rev and the cutting depth of 1 mm for the
contour of actual Y 85.7887 min compared with actual Y that reaches 96.7 the combined plot (d.f). Meanwhile, for the other two combinations of factors (f.v) and (d.v) dark green or tool life above 75 min is very small at 42 mm / min cutting speed. This shows that the two most influencing variables on tool life with minimum variable value at milling machinary using AZ31 magnesium test material and HSS cutting tool are cut the variables of feed motion and cutting depth. That is, the greater the value of feeding motion and the depth of the cut then the more influential in reducing the life of the cutting tool. For variable speed cut, the value of the variable increasingly increasing the value of age response of it. Figure 9: 3D Surface Plot The above 3-dimensional surface illustrates how the combination of the three variables used affects the tool life. Surface number 1 shows that the longest life on the use of high cutting speed variable 42 mm / min and low feeding variable of 0.15 mm / rev. Surface number 2 shows the same thing, the age of the oldest cutting tool using high cutting speed value combined with low cutting depth. Number 3 using low feeding motion with low cut depth also results in the longest life of the cutting tool. Figure 10: Cutting tool using optimization parameters It can be seen that the wear of the tool itself occurs at the end of the edge of cutting tool. This is because at the end of the cut piece has a higher surface than the center
of the cutting tool so that at the end of the cutting
process will experience friction (cut) with the workpiece surface. Use of high cutting speed variable value at this optimum point in accordance with machining tolerance conditions for the finishing process on the milling machine. The cutting speed of 42 mm / min converted to 1280 rpm is the ideal cutting speed according to the HSS diameter tool usage guidelines for final machining process with mixed magnesium or AZ31 materials [9]. It is also revealed by some researchers that relatively large cutting and feeding depths will provide a large cutting load as well and a large contact surface will cause a rise in temperature resulting in a quick tool life due to abrasion and plastic deformation 5. Conclusions From testing to the Central Composite Design application on the optimization of magnesium magnesium machining of AZ31, the following conclusions can be drawn: 1) The optimum value for AZ31 magnesium machining machining using HSS is
using a variable cutting speed of 42 mm / min, a feeding motion of 0. 15 mm / rev, and a cutting depth of
1 mm. 2) The equation of the mathematical model for AZ31 magnesium machining produced from the composite design surface reaction method
is: Y = 34.7 + 7. 69 v - 0. 426 f - 61. 5 d - 0.0688 v * v + 0.000539 f * f + 19.77 d * d
- 0.00352 v *
f - 1. 074 v * d + 0.0363 f * d.
With Y in response to tool life. With the estimated life of the cutting tool obtained from the calculation of modeling is over 85.7887 minutes. 3) The actual life score of the test using the optimum value increased by 9.36% from 85,7887 minutes to 96.7 minutes or 10,9113 minutes. 4) Residual value of 87.4% means response Y (tool life) has a strong relationship to the three variables. 5) The fastest tool life for 4 minutes using a variable combination of
cutting speed 42 mm / min, feeding motion 0.25 mm / rev and cutting depth of
1 mm. While the longest tool life is 96.7 minutes using a combination of variables of the optimal value obtained from the second order mathematical modeling is
cutting speed 42 mm / min, feeding motion 0. 15 mm / rev and 1 mm cutting depth.
6. Acknowledgement
These authors acknowledge the financial support from Directorate General of Higher Education of Ministry of Research and High Education of Indonesia. The acknowledgments also for University of Lampung which facilitated the equipment to finish this experiment. References
[1] S.N. Ranade, P. Thiagarajan, 2017, Selection of design for response surface, IOP conference Series: Material Science and Engineering263, pg. 2-14. [2] Nuryanti, Djati H Salimy. 2008, A Method for response surface and application in optimization of chemical experiment, Conference on computation, science and technology of nuclear, Batan Indonesia. [3] K. Palanikumar, R. Karthikeyan. 2007. Assessment of Factors Influencing Surface Roughness on The Machining of Ai/SiC Particulate Composites. Mater. [4] Netter, J. and W. Wasserman. 1974. Applied Linear Statistical Models, Regression, Analysis of Variance, and Experimental Designs. Richard D. Irwin, Inc., Homewood. Illinois. [5] G.A. Ibrahim, B. Purnomo, A. Hamni, S. Harun, Y. Burhanuddin, 2017, IOP conference Series: Materials and Engineering 344, pg. 1-10. [6] G. A. Ibrahim, C.H. Che Haron, J.A. Ghani, 2010, Taguchi optimization for surface roughness and material removal rate in turning of Ti-6 Al 4 V ELI, International Review of Mechanical and Materials Engineering, Vol. 4, No.2, pg. 216-221. [7] D.C. Montgomery, 1984, Design and analysis of experiments, John Wiley & Sons, Canada. [8] B. Jones, P. Goos, 2011, Optimal design of experiments: A case study approach, Hoboken, NJ: Wiley. [9] K. Kadirgaman, K.A. Abou El Hossein, B. Muhammad, H. Al Ani, M.M. Nur, 2008, Cutting force prediction by FEA and RSM when machining Hastelloy C-22 HS with 90 holder, Journal of Scientific & Industrial Research, Vol. 67, pp. 421-427.
International Journal of Science and Research (IJSR) ISSN: 2319-7064 Index Copernicus Value (2016): 79.57 | Impact Factor (2017): 7.296 International Journal of
Science and Research (IJSR) ISSN: 2319-7064 Index Copernicus Value (2016): 79.57 | Impact Factor (2017): 7.296
International Journal of Science and Research (IJSR) ISSN: 2319-7064 Index Copernicus Value (2016): 79.57 | Impact Factor (2017): 7.296 International Journal of
Science and Research (IJSR) ISSN: 2319-7064 Index Copernicus Value (2016): 79.57 | Impact Factor (2017): 7.296
International Journal of Science and Research (IJSR) ISSN: 2319-7064 Index Copernicus Value (2016): 79.57 | Impact Factor (2017): 7.296
International Journal of Science and Research (IJSR) ISSN: 2319-7064 Index Copernicus Value (2016): 79.57 | Impact Factor (2017): 7.296 Paper ID: ART20191940 DOI: 10.21275/ART20191940 708 Paper ID: ART20191940 DOI: 10.21275/ART20191940 709 Paper ID: ART20191940
Volume 7 Issue 10, October 2018 www.ijsr.net Licensed Under Creative Commons Attribution CC BY DOI: 10.21275/
ART20191940 710 Paper ID: ART20191940
Volume 7 Issue 10, October 2018 www.ijsr.net Licensed Under Creative Commons Attribution CC BY DOI: 10.21275/
ART20191940 711 Paper ID: ART20191940 Volume 7 Issue 10, October 2018 www.ijsr.net Licensed Under Creative Commons Attribution CC BY DOI: 10.21275/ART20191940 712 Paper ID: ART20191940 Volume 7 Issue 10, October 2018 www.ijsr.net Licensed Under Creative Commons Attribution CC BY DOI: 10.21275/ART20191940 713