Design of Experiment in the Milling Process of Aluminum Alloys in the Aerospace Industry

: For many years, surface has quality received a serious attention due to its inﬂuence on various mechanical properties. The main contribution made in this scientiﬁc paper is the performance of actual experiments, as well as the experimental processing obtained in order to develop a model for predicting the surface roughness based on the optimization of cutting parameters. The novelty of this paper is brought by the method of obtaining the regression equation of the surface roughness, resulted from a standard end-milling process (standard milling tools, standard milling parameters, recommended by the tool manufacturer, 3 axis CNC machine and standard vice), on aluminum alloy 7136 in temper T76511, through two statistical methods of data analysis. This material is used for the production of extruded parts and is poorly understood for the proposed line of research. This study’s aim is to determine the surface roughness equation obtained by the milling of aluminum alloy 7136 in two ways: using Taguchi (cid:48) s experimental design once and the other, using the central composite design. The Taguchi method and the central composite design are used to develop an e ﬃ cient mathematical model to predict the optimal level of certain processing parameters. Using ANOVA analysis, a comparative study of calculated and experimental surface roughness values is carried out. The initial characteristics (surface roughness) and the controlled factors (cutting speed, depth of cut and feed) are analyzed with the Minitab program. Finally, an analysis of the advantages and disadvantages of the two methods used is presented. This study has a great industrial application, since the main task of every manufacturer is to achieve a better quality of the ﬁnal product with minimal processing time.

With the Taguchi and RSM technique, Alagarsamyet [13] has conducted the experiment by turning the 7075 aluminum alloy. The author presents an effective approach in order to optimize the cutting parameters (cutting speed, feed rate and feed per tooth) in order to minimize surface roughness and maximize material removal rate. For processing, he used TNMG 115 100 tungsten carbide tool. The author analyzed the performance characteristics in the turning process based on the orthogonal array, the signal/noise ratio and the ANOVA analysis. Finally, he was able to determine a mathematical model of the response surface [13].
Ezuwanizam [14] found that the optimal cutting factors for speed, feed and depth were the optimal life of the TiN coated tool on aluminum 6061. The results show that as the cutting parameter values increase, the tool wear decreases during the final milling. However, the axial cutting depth does not affect the response in the same way as the cutting speed and feed ratio do.
The research in this article begins with the first original contribution made by the authors for this work, namely some comparative graphs about the state of aluminum alloys in the world. The first graphs have been drawn and describe the aluminum alloys used as a percentage in the aerospace industry in the 2005-2019 period (Figure 1).
Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 19 With the Taguchi and RSM technique, Alagarsamyet [13] has conducted the experiment by turning the 7075 aluminum alloy. The author presents an effective approach in order to optimize the cutting parameters (cutting speed, feed rate and feed per tooth) in order to minimize surface roughness and maximize material removal rate. For processing, he used TNMG 115 100 tungsten carbide tool. The author analyzed the performance characteristics in the turning process based on the orthogonal array, the signal/noise ratio and the ANOVA analysis. Finally, he was able to determine a mathematical model of the response surface [13].
Ezuwanizam [14] found that the optimal cutting factors for speed, feed and depth were the optimal life of the TiN coated tool on aluminum 6061. The results show that as the cutting parameter values increase, the tool wear decreases during the final milling. However, the axial cutting depth does not affect the response in the same way as the cutting speed and feed ratio do.
The research in this article begins with the first original contribution made by the authors for this work, namely some comparative graphs about the state of aluminum alloys in the world. The first graphs have been drawn and describe the aluminum alloys used as a percentage in the aerospace industry in the 2005-2019 period ( Figure 1). As our own finding following the analysis of the graph made, it can be seen that the majority of Al6061 reaches 26%, followed by Al7075 at 22%. The aluminum alloy study is also used in the aviation industry. These alloys have been developed by a number of dedicated companies with the help of principal aircraft manufacturers to improve the production process of various aluminum areas.
This study will focus on Al7136, developed and manufactured by Universal Alloy Corporation. This type of material is used in the aircraft industry. This aluminum alloy, relatively newly developed, has superior properties to other aluminum alloys, among which include its high resistance to traction, also to wear, corrosion, its low value of thermal expansion, high durability, ductility and conductivity. All these properties make Al7136 a versatile material [15].
Another original comparative graph made by the authors is focused on the proportionality of the cutting factors impact exerted on the surface quality. As our own finding following the analysis of the graph made, it can be seen that the majority of Al6061 reaches 26%, followed by Al7075 at 22%. The aluminum alloy study is also used in the aviation industry. These alloys have been developed by a number of dedicated companies with the help of principal aircraft manufacturers to improve the production process of various aluminum areas.
This study will focus on Al7136, developed and manufactured by Universal Alloy Corporation. This type of material is used in the aircraft industry. This aluminum alloy, relatively newly developed, has superior properties to other aluminum alloys, among which include its high resistance to traction, also to wear, corrosion, its low value of thermal expansion, high durability, ductility and conductivity. All these properties make Al7136 a versatile material [15].
Another original comparative graph made by the authors is focused on the proportionality of the cutting factors impact exerted on the surface quality.
In Figure 2, this situation is presented. Concerning this case, it can be seen that the most studied parameter is the feed per tooth with 38%, closely followed by the cutting speed with 34% and the cutting depth with 28%.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 19 In Figure 2, this situation is presented. Concerning this case, it can be seen that the most studied parameter is the feed per tooth with 38%, closely followed by the cutting speed with 34% and the cutting depth with 28%. Other comparative original graphs are made by the authors on the most studied research directions on aluminum alloy machining (Figure 3), also on the study of the cutting operations frequency of the aluminum alloys (Figure 4), and finally the mathematical methods used to optimize the aluminum alloy cutting processes ( Figure 5).   Other comparative original graphs are made by the authors on the most studied research directions on aluminum alloy machining (Figure 3), also on the study of the cutting operations frequency of the aluminum alloys (Figure 4), and finally the mathematical methods used to optimize the aluminum alloy cutting processes ( Figure 5).
Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 19 In Figure 2, this situation is presented. Concerning this case, it can be seen that the most studied parameter is the feed per tooth with 38%, closely followed by the cutting speed with 34% and the cutting depth with 28%. Other comparative original graphs are made by the authors on the most studied research directions on aluminum alloy machining (Figure 3), also on the study of the cutting operations frequency of the aluminum alloys (Figure 4), and finally the mathematical methods used to optimize the aluminum alloy cutting processes ( Figure 5).     As Figure 3 shows, the most studied research direction on aluminum alloy machining is represented by the surface roughness with 32%, followed by the cutting forces with 18%, then by the tensions with 11% and by the chip formation with 10%. The friction, temperature, deformation, and the tool wear were studied less than the above-mentioned parameters.
In the cutting operation case, the most studied machining operation on aluminum alloy is the milling operation with 52%, followed closely by turning with 42%.    As Figure 3 shows, the most studied research direction on aluminum alloy machining is represented by the surface roughness with 32%, followed by the cutting forces with 18%, then by the tensions with 11% and by the chip formation with 10%. The friction, temperature, deformation, and the tool wear were studied less than the above-mentioned parameters.
In the cutting operation case, the most studied machining operation on aluminum alloy is the milling operation with 52%, followed closely by turning with 42%.  As Figure 3 shows, the most studied research direction on aluminum alloy machining is represented by the surface roughness with 32%, followed by the cutting forces with 18%, then by the tensions with 11% and by the chip formation with 10%. The friction, temperature, deformation, and the tool wear were studied less than the above-mentioned parameters.
In the cutting operation case, the most studied machining operation on aluminum alloy is the milling operation with 52%, followed closely by turning with 42%.
Finally, the mathematical methods used to optimize the aluminum alloy cutting processes were analyzed, and the results show that the most studied methods are ANOVA with 35%, RSM with 26% and Taguchi with 24%.
We consider Figures 1-5 important because these graphs are created based on a serious topical documentary.
In this scientific paper, we use the Taguchi, the central composite design and ANOVA methods to obtain the optimal conditions for end-milling process of 7136 aluminum alloy used in the aerospace field. The aim is to obtain the contribution percentage of each parameter in order to confirm the optimal conditions obtained by using the Taguchi and the central composite design methods. Table 1 gives a brief presentation of the research papers in which this 7136 aluminum alloy was also studied. Regression analysis, ANOVA [20] This research presents novelty elements in this field due to the experimental programs behind this applied research being permanently improved. Moreover, we consider that the approached subject is very topical, still being associated with the material sampling processes in various industries such as the aerospace industry. We consider that the study we propose represents a topical reference in our field of competence and is argued by topical experimental results that take into account a current stage of knowledge in the field that was the basis of the proposed research. Considering the purpose of this article, which is to determine the surface quality equation produced by Al7136 end-milling, based on the above comparisons, the full test method will be presented.

Experimental Procedure
Experiments were conducted to study the cutting effect of the measurement method: cutting speed, cutting depth and feed, applied to the product response: surface roughness.

Work Material
Tests are performed based on machining of Al7136-T76511 [21]. This alloy is used in aircraft industries due to its properties, such as: • High strength to weight ratio; • High wear resistance; Conductivity, which makes it a versatile material [22].
The Al7136-T76511 is a type of aluminum alloy code 7136. To achieve the T76511 temper, the metal is heat-treated in solution, and stress relieved, after the natural stabilization of over aging. Helping with stress is done by stretching the metal to some degree, depending on the type of product being produced (rack or tube). Aging has been chosen to increase corrosion resistance. The metal is straightened after expansion. This temper stimulus is closely related to T76510, which does not allow such straightening [23].
The chemical composition of the Al7136 conforms to the percentages by weight shown in Table 2, determined in accordance with AMS2355 Standard [24].
According to AMS4415A Standard [23] of the aerospace material specification, the Al7136-T76511 is an aluminum alloy in the form of extruded bars, rods, wire, profiles (shapes) and tubing. In general, these extrusions are found in structural applications that require a combination of high tensile and compressive strength and good corrosion resistance, but the use of these extrusions is not limited to such applications (Table 3).  Extrusions must be heat-treated with solution, stress relieved by stretching after treatment of the solution to produce a permanent set nominal value of 1.5 percent, but not less than 1 percent or more than 3 percent and exceeded by T76511 temper, according to AS1990 [25,26]. Extrusions in the T76511 temper can receive a minor recovery, after stretching, of a required quantity meet the tolerance requirements of 3.6.
Extrusions must comply with the following requirements, determined on the mill product according to AMS2355 [24]. To carry out the tests, the parts have the dimensions 500 × l01 × 24.5 mm: the central composite design and 100 mm × 35 mm and 30 mm: the Taguchi method. Each machined sample was performed according to the cutting procedures set based on the combination of the cutting regime in each methodology case.

Cutting Tool
The test was made with a basic tool for aluminum machining (16 mm cutting tool, 100% engagement, SECO R217.69-1616.0-09-2AN), which has two cutting inserts ISO code XOEX090308FR-E05, H15 [27]. The tool used in the experiment was a brand-new tool and the tool wear was not considered in the study.

CNC Machine
The machine used for testing is a 3-axis HAAS VF2 CNC. The specifications of the CNC machine are shown in Table 4.  The sample was fixed with one clamp on the CNC table (for the Taguchi methodology) three clamps (for the central composite design) respectively, to obtain the rigidity. In this respect, the samples are parallel with the CNC table and perpendicular to the main shaft.
Throughout the tests, large quantities of Blasocut BC 35 Kombi SW coolant were used in the cutting areas. Among the characteristics of the coolant is the pump pressure, which had a value of 8 bar.

Response
This paper's goal is to use the Taguchi method and central composite design to analyze the cutting factors impact effects (cutting speed, cutting depth and feed) generated during the milling process on the 7136-aluminum surface. There are several ways to measure the surface quality of a part. Mathematical measurements (R a ) of the surface were obtained and measured in the center of the machine surface using the surface tester Mitutoyo SURFTEST SJ-210 ( Figure 6).
The measurement tool resolution was set and tested with a certified gage. The measurement tool available at the time when the experiment was made had a tip diameter of 4 µm. The entire study was based on these data. The measurement tool was set to measure only 5 mm, there were seven measurements conducted in each case. The measurement error was not taken into consideration in order to prove the data reproducible. The sampling length was 2.5 mm with a number of sampling lengths × 7. The type of detector on retractable drive unit type was SJ-210 (4 mN type), the type of filtration used was Gaussian, and standard is ISO 1997, as can be seen in Figure 6. In this figure, it can be seen that the cut-off (λc) is equal to 0.8 mm.

Response
This paper's goal is to use the Taguchi method and central composite design to analyze the cutting factors impact effects (cutting speed, cutting depth and feed) generated during the milling process on the 7136-aluminum surface. There are several ways to measure the surface quality of a part. Mathematical measurements (Ra) of the surface were obtained and measured in the center of the machine surface using the surface tester Mitutoyo SURFTEST SJ-210 ( Figure 6). The measurement tool resolution was set and tested with a certified gage. The measurement tool available at the time when the experiment was made had a tip diameter of 4 µ m. The entire study was based on these data. The measurement tool was set to measure only 5 mm, there were seven measurements conducted in each case. The measurement error was not taken into consideration in order to prove the data reproducible. The sampling length was 2.5 mm with a number of sampling lengths × 7. The type of detector on retractable drive unit type was SJ-210 (4 mN type), the type of filtration used was Gaussian, and standard is ISO 1997, as can be seen in Figure 6. In this figure, it can be seen that the cut-off (λc) is equal to 0.8 mm.

Process Variables and Their Parameters
In this article, cutting experiments were designed taking into account three cutting factors: cutting speed (m/min), feed (mm/tooth) and cutting depth (mm). Selected levels for cutting factors are shown in Table 5 and are in accordance with the SECO Equipment Manufacturer′s Guide as well as regarding the machine capabilities and technology, cutting tools and CNC machine. In the Taguchi

Process Variables and Their Parameters
In this article, cutting experiments were designed taking into account three cutting factors: cutting speed (m/min), feed (mm/tooth) and cutting depth (mm). Selected levels for cutting factors are shown in Table 5 and are in accordance with the SECO Equipment Manufacturer s Guide as well as regarding the machine capabilities and technology, cutting tools and CNC machine. In the Taguchi model, the selected levels reflect the minimum and maximum values of the machining factors, according to the test section. In the central composite design, each factor was assigned to the settled values in the experimental field. The original form of the central composite design was chosen-the circumscribed one. The star points are at an alpha distance from the center, based on the properties desired for the design and the number of factors in the design. The star points establish new extremes for the low and high settings for all factors. The surface roughness was determined based on the established parameters as shown in Table 5. For each experiment three surface measurements were performed and then the average of the mean square deviation (R a med) calculation was used, indicating the mathematical mean of the three measurement lines.

Taguchi Design versus Central Composite Design
The design of the experiment is a very strong analysis tool with which it can be modeled and analyzed the influence of the control parameters, which is exerted on the followed response. The standard models are difficult to use, especially on a large number of experiments and when the control factors are varied and numerous [29,30]. This research uses Taguchi methodology and the central composite design to analyze the surface roughness by 7136 aluminum alloy machining as an output variable in end-milling process. The Taguchi method is an effective tool that is widely accepted by industrial engineers to approach the highest possible production at the right price and at the right time. The factors influencing the response are arranged in the form of a lattice square model, this pattern is called an orthogonal array. The design and selection of the orthogonal structure and the reasons for the experiments are the main foundations of the Taguchi process [31].
Malvade and Nipanikar [32] noted that the Taguchi method is more focused on shaping the development of production processes to create high-quality output compared to statistical control systems that attempt to control factors affecting quality.
Moshat [33] demonstrated that the Taguchi method is one of the most effective design test tools to create a high-quality product, developed by Genichi Taguchi. The goals of the orthogonal Taguchi (OA) are a step that gives a small number of very balanced and simultaneous tests.
The controls for this test included: cutting speed, cutting depth and feeding of each tooth. A number of eight experiments, as shows the L8 orthogonal array (Table 6), were obtained by applying the design of experiment (DOE) steps. Following the analyzed output data, the optimal machining condition was deducted. The approach of the problem from the central composite design method perspective consists of the three factors involved, which are taken into account with their corresponding values presented in Table 5, in order to determine their influence level exerted on the response.
The tests were performed respecting the mentioned cutting regimes of the process factors combinations. Minitab 17 design expert software is used to create the tests plan and analyze all responses in a mathematical format.
Overall, eight experiments were carried out for the Taguchi method, each with three R a measurements and a total of 24 measurements (Table 7).
For central composite design results, 125 experiments and a total of 375 measurements were carried out (Table 8). To determine the surface roughness equation, the contribution of each parameter and their interactions must first be determined.

Contribution of Parameters and Their Interactions
A good understanding of the various aspects of different conditions can be seen using the method called ANOVA [5,6]. The purpose of ANOVA is to determine the magnitude associated with each component in the target operation and to reduce the error. ANOVA has also selected the highest quality components from a wide range of options. ANOVA is used to determine which actual metrics affect specified values.
Using the Taguchi method and the central design of the ANOVA analysis, the inclusion and impact of each factor and their interaction with the surface current was determined. Table 9 shows the analysis of variance, using Minitab 17.
The confidence interval in ANOVA was considered to be 95%. In this table (Table 9), the ANOVA analysis revealed that the cutting speed has the highest influence and affects the surface in both cases: Taguchi s method and central composite design.
The reason why the cutting speed has the greatest influence and affects the surface roughness is because if it is not correlated with the rotation speed of the tool, there is a settlement of the processed material that generates tool vibrations and thus leads to higher roughness.
The main contributing factor is the cutting speed and the interaction between the cutting speed and the depth of cut. In this experiment, the effect of the other parameters as well as the interactions between them have a smaller impact on the surface roughness.

The Regression Equation of the Surface Roughness
According to the obtained results obtains by Table 8, the R a regression equation in both situations, the Taguchi method and central composite design, was determined. Using Minitab 17, the surface roughness equation for Taguchi method is (1): Using Minitab 17, the surface roughness equation (2) for central composite design (CCD) is: The normal probability plot in both cases Taguchi and CCD, are presented in Figures 7 and 8. Using the Minitab software, the regression equations related to the R a surface roughness were determined. The aim is to describe the relationship between the answer (R a ) and the terms in the model (cutting speed, depth of cut, feed per tooth). The regression equation is an algebraic representation of the regression line. In the regression equations, the numerical values represent the estimated coefficients for the terms in the model. These coefficients were calculated based on the statistical methods applied in this scientific research paper.

Comparison Between the Two Regression Equations Determined
To make a comparison between the accuracy of these two determined equations using Taguchi′s method and central composite design, Table 10 presents the surface roughness measured values. The surface roughness relative error was calculated between the measure's values and the calculated values of Ra in both situations (Taguchi′s method and central composite design).

Comparison Between the Two Regression Equations Determined
To make a comparison between the accuracy of these two determined equations using Taguchi s method and central composite design, Table 10 presents the surface roughness measured values. The surface roughness relative error was calculated between the measure's values and the calculated values of R a in both situations (Taguchi s method and central composite design).

Results and Discussions
After the regression equation determining for the R a , the results were predicted at any area of the experimental domain, based on the determined regression models. Thus, the R a values of the surface profile were determined using the obtained regression equations. The R a calculated values results afferent to the R a measured values are shown in Table 10.
Starting with these calculations, the comparative graphical representations were made between the experimentally determined measurements and the calculated values using the regression equation determined by the Taguchi method and the central composite design (Figure 9).

Results and Discussions
After the regression equation determining for the Ra, the results were predicted at any area of the experimental domain, based on the determined regression models. Thus, the Ra values of the surface profile were determined using the obtained regression equations. The Ra calculated values results afferent to the Ra measured values are shown in Table 10.
Starting with these calculations, the comparative graphical representations were made between the experimentally determined measurements and the calculated values using the regression equation determined by the Taguchi method and the central composite design (Figure 9).     Based on the graph analysis, it was found that the calculated arithmetic means deviations of the surface profile based on the regression equations approximate the experimental values with a total average error of 22% for the Taguchi′s method and 27% for the central composite design.
Divided by cutting speed intervals, this error accumulates the averages of the following errors presented in Table 11.
The error problem is generated by the values of 570 m/min and 610 m/min. At these cutting speeds, the average roughness of the area, measured by experiments, registers the critical distribution. The roughness value increasing was generated by the vibrations as a result of the machining. It was found that the poorest quality results at 570 m/min and 610 m/min cutting speed. The values of the surface roughness recorded at these speeds are quite high compared to those at lower speeds and upper speeds, respectively.  Based on the graph analysis, it was found that the calculated arithmetic means deviations of the surface profile based on the regression equations approximate the experimental values with a total average error of 22% for the Taguchi s method and 27% for the central composite design.
Divided by cutting speed intervals, this error accumulates the averages of the following errors presented in Table 11. The error problem is generated by the values of 570 m/min and 610 m/min. At these cutting speeds, the average roughness of the area, measured by experiments, registers the critical distribution. The roughness value increasing was generated by the vibrations as a result of the machining. It was found that the poorest quality results at 570 m/min and 610 m/min cutting speed. The values of the surface roughness recorded at these speeds are quite high compared to those at lower speeds and upper speeds, respectively.
Vibration events lead to a rough surface. This vibration is the effect of a resonance phenomenon given by tool (piece) materials used. The vibration has not been measured during the experiment, but the statement is based on the fact that all other experiment conditions were respected on all combinations: the same CNC machine, the same setup, the same type of material (certified material by lab tests, mechanical and chemical test). The causes, consequences and production process have to be studied further.
Several papers dealing with this subject have been identified in the literature. For example, [34] in his paper presents the effects of the spindle attributed forced vibrations on the processing characteristics of the vertical milling process. The effects of three spindle levels attributed to forced vibrations together with feed rate and axial cutting depth are evaluated on surface roughness, dimensional accuracy and tool wear under constant conditions of radial cutting depth and cutting speed. He found that the vibration amplitude of machine tools and the axial cutting depth are statistically significant at a 95% confidence level for surface roughness, the vibration amplitude being the most important factor followed by the axial cutting depth. It is found that higher values of vibration amplitude and feed speed result in excessive tool wear, with the vibration amplitude combined with the feed rate and axial depth, resulting in a catastrophic damage to the tool.
Another research belongs to [35], who found that the profile milling processes are very sensitive to vibrations caused by the cutter leakage, especially when it comes to operations in which the diameter of the cut varies on a scale of a few millimeters. The aim of his research was to experimentally analyze the effect of cutter runout on cutter vibration and how it affects chip removal and therefore the topomorphy of the workpiece. He evaluated the effect of vibration phenomena, caused by cutter runout, on the workpiece topomorphy in end-milling.
Overall, Figure 11 shows the significant spatial variation related to cutting speed and feed per tooth. The graph analysis highlights that the speeds of 570 and 610 m/min in addition to a small feed showed an effect on R a values, which increased in all experiments. We suppose that the vibration may be the reason for this increase. Figure 12 shows the diagrams of the constant level cycles, from which the gradual values increase with increasing cutting speed and feed per tooth value.
caused by cutter runout, on the workpiece topomorphy in end-milling.
Overall, Figure 11 shows the significant spatial variation related to cutting speed and feed per tooth. The graph analysis highlights that the speeds of 570 and 610 m/min in addition to a small feed showed an effect on Ra values, which increased in all experiments. We suppose that the vibration may be the reason for this increase. Figure 12 shows the diagrams of the constant level cycles, from which the gradual values increase with increasing cutting speed and feed per tooth value.   experimentally analyze the effect of cutter runout on cutter vibration and how it affects chip removal and therefore the topomorphy of the workpiece. He evaluated the effect of vibration phenomena, caused by cutter runout, on the workpiece topomorphy in end-milling.

Conclusions
Overall, Figure 11 shows the significant spatial variation related to cutting speed and feed per tooth. The graph analysis highlights that the speeds of 570 and 610 m/min in addition to a small feed showed an effect on Ra values, which increased in all experiments. We suppose that the vibration may be the reason for this increase. Figure 12 shows the diagrams of the constant level cycles, from which the gradual values increase with increasing cutting speed and feed per tooth value.

Conclusions
This study's aim was to determine the R a equations by dimensional process measurement methods in two ways: first using the Taguchi design of experiments and second using the central composite design.
Analysis of variance (ANOVA) is performed to identify key variables and clarify their impact on response characteristics.
The conclusion of both cases is the same: the cutting speed is the factor which has the highest effect on the end-milled surface. It can be seen by the percentage effect of each factor on the surface that there is a very weak correlation between the control factors affecting the surface quality.
The other two parameters, have a meaningless contribution (less than 1%) and can be forgotten.
By comparing relative errors between two measurement equations on the R a scale it can be seen εx for the Taguchi method, the median value of relative errors is 22% and for the central composite design εx the relative error is 27%.
In general, the values derived from the central composite design are closer to the measured roughness.
The main R a advantage of the Taguchi method is the reduction in the number of tests, lower costs and shorter time. The disadvantages include the fact that this method is not as good as the central composite design.
On the other hand, the advantage of the central composite design is the accurate comparison according to the Taguchi method. The disadvantages include the large number of tests, the cost of the tests, and the extra time spent on the tests.
It is difficult to say which method is the best. The selection belongs to the researcher and depends on the research experience, time and resources, as well as how accurate the results should be.
As a further research direction, there is the possibility of extending the studies and the research, taking into account other parameters and other indicators in a more complex form.
The vibration leads to the rough surface and is given by the resonance phenomenon of tool (piece) materials used. This can be a direction for further research because the causes, consequences and production process have to be studied further.