Optimization of cutting forces and surface roughness via ANOVA and grey relational analysis in machining of In718

: Machinability and optimization are the two objectives of researchers who guide us to enhance the manufacturing industry. Examining and analyzing the parameters such as surface roughness, tool wear, and cutting force during the processing would be bene ﬁ cial that are used in various ﬁ elds in the manufacturing industires. This study examined the e ﬀ ect of cutting forces to surface roughness on the material surface. Experimental studies were carried out by using constant feed rate ( 0.1 mm/rev ) , depth of cut ( 1 mm ) , three di ﬀ erent coolants ( CO 2 , minimum quantity lubrication, and dry ) , and cutting speeds ( 100, 140, 180, 220 m/min ) . In this study, grey relational analysis modeling and analysis of relationships between F x , F y , and F z forces on the surface roughness of Inconel 718 material, which is an important alloy in aviation, is examined. The in ﬂ uence of machin - ability parameters on F top and R a was calculated using variance analysis, which determined that cutting speed was the most signi ﬁ cant machining parameters.


Introduction
Because of cost, product quality, and other parameters which are significant factors for utilization areas, material choice, and production rate, metal cutting efficiency and machine parameter optimization have become increasingly important as the manufacturing industry has grown significantly.One of the most broadly adopted machining processes for transforming a material into the required geometric shape is machining.The problematic areas are machined with a cutting tool that is harder and tougher than the material throughout the cutting process.High cutting forces resulting from friction between the cutting tool and the material surface have a direct impact on tool life and surface quality.The heat generated during the chip removal operation should be managed to prolong the life of the cutting tool and improve the surface quality of the materials [1][2][3][4].
Becasue of their chemical and physical attributes, superalloys are difficult to process, but they are highly preferred materials [5][6][7].Furthermore, the machinability, hardness, as well as other properties of materials can be modified by introducing elements such as sulfur and selenium into composition [8][9][10][11].These materials are composed of nickel-iron and one of the base superalloys, Inconel 718 (2.4668), is employed in a variety of critical applications [12].Owing to the elements added to the Inconel 718 alloy, it gains properties such as high temperature, corrosion, cracking, and fatigue characteristics, whereas these elements make Inconel's machinability more difficult and increase the machining cost.Many academic studies have been undertaken in recent years to investigate the effects of cutting parameters on cutting forces and surface roughness that occur during the machining of Inconel 718.High temperature, cutting tool wear, and chemical reaction susceptibility between the cutting tool and the material during the cutting process are the key issues encountered while machining Inconel 718 [13].Machinability of superalloy materials in manufacturing can be improved through appropriate parameter assessment, cutting tool configuration, and lubrication methods, among many other things.During the cutting of the material, rpm, feed rate, depth of cut, and other parameters are described in the literature.When reviewing studies on the effects of parameters, Swamy et al. found that cutting tool wear is less between 225 and 450 rpm, and the surface roughness decreases as the rpm increases in their study on Alloy (Inconel) 718.He also noticed that when the feed rate was increased from 0.1 to 0.3 mm, the surface roughness (R a ) increased dramatically [14].Panadian and Rout deployed a carbon-coated drill as a cutting tool on Inconel 718 and established that the surface roughness (R a ) decreased with higher cutting speed (700 rpm), feed rate (20 mm/min), and low depth of cut (0.2 mm).They further demonstrated that a low cutting speed (500 rpm) and a depth cut (0.4 mm) resulted in minimum cutting tool wear [15].Due to its low heat conductivity, Inconel 718 can achieve high temperatures of 900-1,300°C during manufacturing.Throughout machining, the insert is exposed to these high temperatures, bringing challenges with surface topography and dimensional accuracy, as well as a significant decrease in tool life [16,17].
While determining the most efficient cutting parameters for sustainable machining and limited resources in our world, it is essential to identify optimum parameters.The grey relational analysis (GRA) method, one of the optimization approaches, determines the optimum values of the parameters, which are calculated with an accuracy rate depending on the percentage of experiments.The influence of the parameters that should be performed to achieve the intended material integrity was investigated in research focusing on these outcomes, and they concluded that the feed rate was 63.7% performance parameters, the depth of cut was 19% effective, and the cutting speed was 6.9% effective.The grey relational grade (GRG) score improved by 0.563 points as a result of the confirmation experiment conducted upon those data [18,19].Based on the results of the validation experiments they executed as a result of the grey analysis, Ramesh et al. stated that feed rate, cutting speed, and depth of cut had also grown massively in material quality [20].The cutting parameters have been optimized using a variety of approaches, including CCD, RSM, ANN, and GRA.According to Ma et al. energy consumption, surface roughness, and machining duration can all be minimized by 4-40% by optimizing the cutting conditions while processing the material [21].As a result of the GRA analysis they performed on Pekşen and Kalyon AISI 430 stainless steel, the GRG values increased by 0.387, creating a great effect of 69.1% [22].There are many studies in the literature regarding the machining of metals under cryogenic conditions.However, in contrast to metals, studies in relation to the optimazation of machining super alloys are limited.
In this study, Inconel 718 was assessed at several cutting speeds (100-140-180-220 rpm) and with three different coolants (dry stock removal, CO 2 , and minimum quantity lubrication [MQL]).Afterward, utilizing GRA, ANOVA, and regression methods, the influences of these variables on cutting forces and surface roughness were determined, and optimization was performed.

Materials and methods
The material used throughout the experiment was Inconel 718 super alloy, which has a diameter of 50 mm and a length of 200 mm.Table 1 summarizes the chemical specifications of the material investigated in this research.Nickel, iron, and chromium are the primary components of Inconel 718, as can be seen in the composition.As a result, it generates a hard alloy with a low convection coefficient and a high heat resistance [23].
MQL provides a balanced lubricant and air mixture as well as a very low aerosol spray to the machining zone [24,25].Thirty-two experiments were carried out using the cutting speed and cooling processes that employed, and the determined the force values (F x , F y , and F z ) in the X, Y, and Z axes, as well as the surface roughness (R a ) values, were obtained.Figure 1 represents the equipment and experimental setup.
The cutting fluid was mixed with air at 6 bar using a nozzle and an air compressor in the MQL system and afterward supplied to the workpiece-cutting tool interface as shown in Figure 2. The machining experiments utilized three different types of lubricants (dry, MQL, and CO 2 ), two different lubricant flow rates (20 and 40 mL/h), and four different cutting speeds (100, 140, 180, and 220 m/min).Cutting speeds, depth of cut, and feed rate have been determined according to the tool manufacturer (SUMITOMO).The turning experiments used a constant feed rate f = 0.1 mm/rev and a constant depth of cut at = 1 mm.The manufacturer's suggested handbook was used to select process parameter settings.
Cutting tools were provided from ISO CNMG 12 04 08 MM SUMITOMO.The reason for choosing these tools is that it has been observed in different studies that they have very positive effects on both the flank wear on the cutting edge and the surface quality of the workpiece [14,15,17].An x-z axis CNC from Johnford and a Mahr perthometer/M1 type micro-hardness analyzer were included in the experiments.For the cutting force measurement, the Kistler 9121 dynamometer system was used, together with a Kistler 5019 charge amplifier and DynoWare software.
The cutting parameters of the CNC machined Inconel 718 material are listed in Table 2.
Cutting forces were measured during the manufacturing process, and surface roughness values were obtained following this investigation.The data received were then exposed to ANOVA, regression analysis, and GRA processes in order to correlate the factor levels seen in the Taguchi experimental design.Experimental steps has demonstrated in Figure 2.
Classical experimental design methodologies are timeconsuming and costly to implement in industrial applications.As a result, it may be quicker and more efficient to use the Taguchi approach to reduce the number of experiments.As a result of pre-experiment investigations, a significant Optimization of cutting forces and surface roughness  3 decrease in the number of experiments can be accomplished by executing selected experiments instead of full factorial experiments.This method involves assessing an equivalent number of samples for various factor values, with each parameter influencing the results.An orthogonal design was created using Taguchi's experimental design L32, and the factors and levels are listed in Table 2.
The Taguchi experimental data were evaluated by adapting it to a signal-to-noise ratio (S/N).The S/N ratio is the proportion of the experimental results to a factor that has no effect on the experimental design but has an influence on the test results.Because it is important to minimize cutting forces and surface roughness, the maxim "smaller is better" was chosen for this investigation.The following equation was used to calculate the S/N ratio [23]: In addition to the ANOVA method, the GRA approach was also used in parameter optimizations within the scope of the study.GRA is a decision-making method, and the procedures in the calculation can be seen in the following equation: One of the standard operating procedures with normalization approaches is linear data preprocessing.For surface roughness and cutting forces, "smaller is better" normalization was adopted in this investigation.When surface roughness and cutting forces were linearly normalized, values with small ratios would be close to 1 and values with large ratios would be close to 0. A normalization operation was performed under the condition of "smaller is better," as shown in the following equation: The resulting row of the series of length n is represented by the symbol "k." Equations (4) and (5) are used to calculate the grey relationship coefficient at point (k): , , ζ notation is a coefficient between 0 and 1.The ζ notation determines the difference between n k i 0 ( ) and n max .Studies show that the ζ ratio does not affect the rating after the GRG calculation.GRG is calculated by the following equation: The proper experiments that would produce the conditions where the R a and F top values would be the minimum could be listed by sorting the coefficients acquired with the GRG according to "the smallest is better."Idealized parameters comprising two result functions and two optimization procedures were identified, and the three best experimental parameters were determined and compared with the ANOVA analysis.

Results and discussions
Cutting forces were measured using a dynamometer, which can collect force data in three axes while machining.The surface roughness of the processed materials was then calculated as R a .It has been discovered that cutting forces and surface roughness might well be minimized by maintaining the machining parameters at optimal values.R a values were evaluated following machining processes in this investigation.According to the literature, the 1 mm chip amount provided adequate surface quality [26,27].For each cutting process, a new, non-reused cutting tool was chosen.To generate realistic surface roughness values, roughness values were averaged for different areas of the surface.
Taguchi L32 was performed within the scope of the investigation using a mixed-type experimental design.Machinability experiments were conducted utilizing two different cutting tools, four different coolants, and four different cutting rates.For the same type of material, all experiments were accomplished by subtracting the same amount of materials.Table 3 represents the test results.In Table 3, meanings of forces are F x feed force, F y radial force, and F z cutting force.6  Gültekin Basmacı et al.

ANOVA and regression analyses
In the test results, resultant cutting forces F top were found to be in the range between 553 and 1,471 N. Simultaneously, the surface roughness R a varied between 0.288 and 2.199 µm.Cutting speed, cutting tool, and coolant had an effect on alterations in cutting forces and surface roughness values.The effects of the parameters on the findings were determined within the scope of the study employing ANOVA and regression analyses.The R2 regression value of cutting forces was calculated to be 93.02%.The surface roughness R 2 was calculated to be 94.66%.Figures 3 and 4 show the relationship between cutting forces and surface roughness with parameters as a consequence of these experiments.
It has been discovered that the type of cutting tool has the biggest influence on cutting forces.The coolant with the lowest effect was selected.Cutting speeds have a smaller effect compared to cutting tool types.On the other hand, it has been determined that the coolant has a significant effect on the surface roughness, which is the inverse of the cutting forces.The surface roughness was also significantly affected by the tool geometry type and cutting speeds.Nonlinear parameters that may have an effect on F top and R a were defined in addition to those variables for ANOVA analysis.As a result, the opportunity to improve the performance of the analysis was found.ANOVA analysis was used to evaluate the effect of the parameters for the cutting forces, as shown in Table 4.As seen in Figure 4, the ANOVA analysis exposed that the cutting tool had the biggest impact on the cutting forces.Moreover, the nonlinear parameters such as "Coolant*Coolant*cutting tool" and "Coolant*cutting speed" influenced the difference in cutting forces significantly.
Nonlinear parameters have been determined for R a as well as for determining the parameters affecting the cutting forces.The ANOVA analysis results for surface roughness are given in Table 5.The three parameters that have the greatest effect on the surface roughness were determined as coolant, "coolant*cutting tool," and "coolant*cutting speed."It has been observed that ANOVA analyses with dependent variables have similarly performed in recent studies [28].Coolant is a dependent variable, like nonlinear parameters.The linear or nonlinear dependent properties of the cutting forces have essentially little effect on the surface roughness.
The effects of machinability parameters on R a and F top with models produced by ANOVA and regression analyses are shown in Figure 5.According to the results, the changes in cutting tools and coolants caused similar changes on R a and F top .At the same time, increasing cutting speeds resulted in a decrease in R a and an increase in F top .
The analysis of the S/N curves are obtained and displayed in Figure 6.It has been understood that the surface roughness of R a changes at high rates with the Optimization of cutting forces and surface roughness  7 change of the coolant, and the effect of the change in the cutting tool type on R a was the lowest.Obtained data were also consistent with previous results.The purpose of the optimization research conducted after the ANOVA analysis is to minimize the R a and F top values.According to the investigation, the optimum cutting force and surface roughness were obtained at 220 m/min cutting speed and 40 mL/h MQL cooling conditions for both cutting tools.F top and R a were obtained as 805 N and 0.797 µm, respectively, using optimal parameters.The optimal roughness values for In718 material have been determined to be higher than the machining procedures in recent years [19,29].ANOVA optimization study is presented in Figure 7.

GRA
The GRA approach was used in this study to determine the optimal parameters based on the machinability criteria and surface roughness of Inconel 718 nickel-based superalloy.The aim is to decrease both F top and R a values.Normalization techniques were used to generate grey correlation coefficients, and performance rankings were derived by comparing 32 experiments.Table 6 shows the GRA coefficients, S/N ratios, and success rankings based on the test results for all studies.Examining the parameters of the three best tests demonstrated that the cutting tool No. 2, cutting speed of 220 m/min, and cooling conditions with 20 mL/h MQL exposed the best results.F top and R a were, respectively, calculated as 611 N and 0.501 µm.
When both the ANOVA analysis and the GRA data were considered, it was concluded that a cutting speed of 220 m/min and MQL cooling conditions were appropriate.GRA resulted in 59% better R a and 31% better F top outcomes.The parameters influencing surface roughness and cutting forces were established by reviewing the GRG values and delta data obtained with GRA.The GRG analysis is shown in Table 7.It has been observed that cutting speed has a greater impact on the results than cutting tool type and coolant.A similar result was found in the literature studies and the ANOVA analysis [30,31].It is also important that interesting results were obtained in some other works .

Conclusions
Machinability experiments on Inconel 718 nickel-based superalloy were performed in this article, considering  Optimization of cutting forces and surface roughness  9 the cutting speed, cutting tool type, and coolant.The analysis was used to optimize the parameters by comparing the experimental results and the established models.It has been determined that the results acquired from the developed models and the experimental results are completely inclusive.Surface roughness and cutting forces were used to guide the investigations.In the experiments, ANOVA, regression analysis, and the GRA method were performed.In tests 20, 23, and 24, which were completed in accordance with the L32 Taguchi design, results were achieved in which R a and F top were both minimized.Cutting speeds have the highest effect on the results, and the optimum was determined as 220 m/min.Coolant and cutting tool types had similar weight results and were optimized as 20 mL/h MQL and tool type 2, respectively.However, it was determined that the surface roughness and cutting forces were improved at high levels by using the optimized parameters of the Taguchi-assisted GRA analysis.According to the results, the processing of Inconel 718 superalloys shows that the performance values can be improved significantly in further studies by using GRA and ANOVA in the literature.Processing cutting speeds at higher levels to improve surface roughness concerning optimization is in line with studies in the literature.

Figure 2 :
Figure 2: Workflow of the study.

Figure 3 :
Figure 3: Relation of resultant cutting forces with machinability parameters.

Figure 4 :
Figure 4: Relation of surface roughness with machinability parameters.

Figure 5 :
Figure 5: Effect of machinability parameters on F top and R a .

Table 1 :
Machining input process parameters

Table 2 :
Factors and grades in Taguchi experimental design

Table 3 :
Experimental results

Table 4 :
ANOVA results for F top

Table 5 :
ANOVA results for R a

Table 6 :
Results of GRA

Table 7 :
Response table for GRG