1. Introduction
The high-strength material Inconel 718 is a member of the class of nickel-based heat-resistant alloys. Its great strength and creep resistance at high temperatures, among other mechanical and physical attributes, make it a popular material in the aircraft industry for parts that are used in the hot region of turbine engines [
1]. Inconel 718 is regarded as a difficult-to-machine material as it exhibits low heat conductivity as well as the capacity to be strain-hardened [
2]. It can be difficult to achieve the necessary dimensional precision and surface finishing when machining this alloy. When turning, suitable cutting parameters and specialized tools can be used to affect the precision and roughness of the measured dimensions [
3]. The geometry of the cutting edge, the feed rate, the cutting speed, and the depth of cut all have a significant impact on performance measures like surface roughness, cutting force, tool wear, and residual stress on the machined surfaces of Inconel 718 alloy [
4]. Prior research has documented that an increased nose radius has a favorable impact on surface roughness [
5,
6]. Thus, in their study of the machining of Inconel 718 [
5], found that with an increase in tool nose radius, the tool–workpiece friction increased. Therefore, the cutting temperature increased due to friction and resulted in thermal softening on the machined surface, which reduced the degree of work hardening on the machined surfaces of Inconel 718 alloy [
4].
The importance of these parameters is considerable in industries such as automotive, aerospace, and machine and mold manufacturing as they serve as a critical indicator of surface stability throughout the assembly process [
7]. To remain competitive with mass production, industries desire a material removal rate (MRR) that is high enough to ensure that product quality is not compromised within a short time. Quality cutting tools with a high resistance to wear (VB) are, therefore, required to facilitate a shorter machining time and a prolonged tool life of the cutting tool [
8]. Scientific techniques based on Taguchi have been developed to optimize a single performance feature to reduce these machining issues; multiple performance optimization is not applicable for these techniques [
9]. The methodology generates optimal operating conditions for each response variable when multiple response variables are associated with the same conditions as independent variables; however, these conditions may vary among one another [
10]. Consequently, an enhancement in one performance attribute could potentially result in a decline in another performance attribute.
Therefore, the process of optimizing multiple performance characteristics is inherently more complex than optimizing a single characteristic [
11,
12]. The interrelation among multiple factors in a complex process like machining is often ambiguous. Grey systems are frequently used to refer to those that provide inaccurate, insufficient, and ambiguous data [
13]. To address this type of issue, grey relational analysis (GRA) is an essential technique. Deng [
14] introduced the utilization of GRA in addressing engineering challenges by demonstrating its efficacy in managing information that is inadequate, insufficient, and ambiguous. GRA is used to effectively resolve the intricate interrelationships between numerous performance characteristics.
The following were the primary goals of the current study:
Determining the minimum or maximum required values of individual characteristics such as surface roughness, tool wear, cutting time, and material removal rate using a single-objective function, which involved setting the best possible combinations of levels of process control parameters for the Inconel 718 superalloy during finished turning in a CNC machine.
Determining the optimal combination of control factor levels to evaluate the performance of the characteristics in a scenario where both (minimum and maximum) are simultaneously considered for optimization.
Identifying the most important machining parameters and the impact of each process parameter on the machining process’s performance attributes.
The structure of this paper is illustrated in
Figure 1, which shows the process flow diagram and experimental setup used to carry out the investigation.
4. Conclusions
In this study, surface roughness, tool wear, material removal rate, and cutting time were optimized in terms of cutting speed, feed rate, depth of cut, and tool nose radius at three levels during the turning of an Inconel 718 superalloy. Optimization was achieved in two steps: first, each response was optimized as a mono-objective using the signal-to-noise-ratio-based Taguchi method; then all replies were optimized as multi-objectives using the grey relation grade-based Taguchi methodology.
The following conclusions were drawn based on the single- and multi-objective optimization results:
The following parameters produced minimal surface roughness of 0.167 µm, according to the single-objective optimization results: 100 m/min cutting speed, 0.091 mm feed rate, 0.2 mm depth of cut, and 0.8 mm nose radius. Although the tool wear minimum of 44.65 µm required a 60 m/min cutting speed, 0.091 mm feed rate, 0.2 mm depth of cut, and 0.8 mm nose radius, a minimal cutting time of 19.72 s was obtained when the cutting speed was 100 m/min, the feed rate was 0.091 mm/rev, and the depth of cut was 0.4 mm. Similarly, a maximum material removal rate of 4550 mm3/min was produced when a cutting speed of 100 m/min, a feed rate of 0.091 mm/rev, and a depth of cut of 0.4 were combined.
The combination indicated as S3F1D3R1 produced the best values for the turning parameters during the multi-objective optimization, allowing for the desired performance characteristics to be realized.
The results of multi-objective optimization showed that when the Inconel 718 superalloy is turned at a cutting speed of 100 m/min, a feed rate of 0.051 mm/rev, a depth of cut of 0.4 mm, and a tool nose radius of 0.4 mm, all investigated response characteristics reached their optimal values (minimum/maximum) during simultaneous optimization.
Thus, an experimental test was conducted to validate this technique. The grey relational grade, or the overall quality characteristic, was found to improve at ideal values by 0.225—i.e., 22.5%—over the initial parameter settings and by 0.062—i.e., 6.2%—over the best initial parameters.
Based on the ANOVA of the GRG results, it was discovered that the most important factor influencing multiple performance characteristics was depth of cut, which contributed 69.30%, followed by cutting speed (14.52%), nose radius (11.87%), and feed rate (3.79%).
The outcomes derived from this study exhibited a high degree of concordance with the findings of the majority of the cited studies.
The utilization of the adopted single-objective and multi-objective optimization techniques may enable the optimization of distinct responses during the cutting process of various materials and under varying conditions.
In future research, we will compare the results produced using GRA with other optimization techniques (e.g., CFD, artificial neural networks, genetic algorithms, etc.).
Author Contributions
Conceptualization, F.Z. and K.K.; methodology, F.Z.; software, G.T.; validation, F.Z., F.A. and K.K.; formal analysis, K.K.; investigation, F.Z.; resources, F.Z.; data curation, F.A.; writing—original draft preparation, F.A.; writing—review and editing, F.A.; visualization, G.T.; supervision, K.K.; project administration, F.A. All authors have read and agreed to the published version of the manuscript.
Funding
This research received no external funding.
Data Availability Statement
The raw data supporting the conclusions of this article will be made available by the authors on request.
Conflicts of Interest
The authors declare no conflicts of interest.
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Figure 1.
Process flowchart used to conduct the research.
Figure 2.
Main effects plot for S/N ratios: (a) surface roughness, (b) tool wear, (c) material removal rate, and (d) cutting time.
Figure 3.
Contour plots for surface roughness.
Figure 4.
Contour plots for tool wear.
Figure 5.
Contour plots for cutting time.
Figure 6.
Contour plots for material removal rate.
Figure 7.
Main effects plot for means of GRG.
Table 1.
Chemical composition of Inconel 718.
C | Si | Mn | Al | Co | Cr | Fe | Mo | Nb | Ni | Ti | Se |
---|
0.03 | 0.06 | 0.07 | 0.49 | 0.25 | 19.3 | 17.3 | 3.3 | 5.28 | 52.9 | 0.96 | ≤3 |
Table 2.
Mechanical properties of Inconel 718.
Tensile Strength (Mpa) | Yield Strength (Mpa) | Young’s Modulus (Mpa) | Density (Kg/m3) | Melting Point (°C) | Hardness (HBW) | Hardness after Heat Treatment (HBW) | Thermal Conductivity (W/Mk) |
---|
1197 | 1248 | 205 × 103 | 819 | 1290 | 245 | 411 | 11.20 |
Table 3.
Machining parameters and their levels.
Cutting Parameters | Notation | Unit | Levels |
---|
1 | 2 | 3 |
---|
Cutting speed | S | m/min | 60 | 80 | 100 |
Feed rate | F | mm/rev | 0.051 | 0.071 | 0.091 |
Depth of cut | D | mm | 0.2 | 0.3 | 0.4 |
Nose radius | R | mm | 0.4 | 0.8 | 0.4 |
Table 4.
Coded experimental and natural matrix layout using an L9 orthogonal array for Ra and MRR.
Exp. No. | Coded Matrix | Natural Matrix | | Responses | |
---|
Abbreviation | S | F | D | R | Ra | VB | MRR | CT |
---|
Unit | m/min | mm/rpm | mm | mm | µm | µm | mm3/min | s |
---|
1 | 1 | 1 | 1 | 1 | 60 | 0.051 | 0.2 | 04 | 0.198 | 61 | 306 | 58.64 |
2 | 1 | 2 | 2 | 2 | 60 | 0.071 | 0.3 | 0.8 | 0.225 | 65 | 1278 | 42.12 |
3 | 1 | 3 | 3 | 3 | 60 | 0.092 | 0.4 | 0.4 | 0.237 | 67 | 2730 | 32.87 |
4 | 2 | 1 | 2 | 3 | 80 | 0.051 | 0.3 | 0.4 | 0.198 | 90 | 1224 | 43.98 |
5 | 2 | 2 | 3 | 1 | 80 | 0.071 | 0.4 | 0.4 | 0.221 | 98 | 2840 | 31.59 |
6 | 2 | 3 | 1 | 2 | 80 | 0.092 | 0.2 | 0.8 | 0.179 | 63 | 728 | 24.65 |
7 | 3 | 1 | 3 | 2 | 100 | 0.051 | 0.4 | 0.8 | 0.211 | 111 | 2550 | 35.19 |
8 | 3 | 2 | 1 | 3 | 100 | 0.071 | 0.2 | 0.4 | 0.175 | 113 | 710 | 25.27 |
9 | 3 | 3 | 2 | 1 | 100 | 0.092 | 0.3 | 0.4 | 0.195 | 108 | 2730 | 19.72 |
Table 5.
Response table for Ra.
Factors | Mean of Means | Mean of S/N Ratio |
---|
Level | S | F | D | R | S | F | D | R |
1 | 0.2133 | 0.1980 * | 0.1780 * | 0.2023 | 13.46 | 14.07 * | 15.00 * | 13.92 |
2 | 0.1967 | 0.2037 | 0.2027 | 0.1980 * | 14.17 | 13.87 | 13.87 | 14.11 * |
3 | 0.1927 * | 0.2010 | 0.2220 | | 14.33 * | 14.01 | 13.09 | |
Delta | 0.0207 | 0.0057 | 0.0440 | 0.0043 | 0.87 | 0.21 | 1.91 | 0.19 |
Rank | 2 | 3 | 1 | 4 | 2 | 3 | 1 | 4 |
Table 6.
Response table for VB.
Factors | Mean of Means | Mean of S/N Ratio |
---|
Level | S | F | D | R | S | F | D | R |
1 | 64.33 * | 87.33 | 79.00 * | 89.50 | −36.16 * | −38.57 | −37.58 * | −38.81 |
2 | 83.67 | 92.00 | 87.67 | 79.67 * | −38.30 | −39.05 | −38.67 | −37.72 * |
3 | 110.67 | 79.33 * | 92.00 | | −40.88 | −37.73 * | −39.08 | |
Delta | 46.33 | 12.67 | 13.00 | 9.83 | 4.72 | 1.32 | 1.50 | 1.09 |
Rank | 1 | 3 | 2 | 4 | 1 | 3 | 2 | 4 |
Table 7.
Response table for MRR.
Factors | Mean of Means | Mean of S/N Ratio |
---|
Level | S | F | D | R | S | F | D | R |
1 | 1438.0 | 1360.0 | 581.3 | - | 60.19 | 59.87 | 54.66 | 62.50 |
2 | 1597.3 | 1609.3 | 1744.0 | - | 62.69 | 62.74 | 64.20 | 62.50 |
3 | 1996.7 * | 2062.7 * | 2706.7 * | | 64.63 * | 64.90 * | 68.64 * | |
Delta | 558.7 | 702.7 | 2125.3 | - | 4.44 | 5.03 | 13.98 | 0.00 |
Rank | 3 | 2 | 1 | 4 | 3 | 2 | 1 | 4 |
Table 8.
Response table for CT.
Factors | Mean of Means | Mean of S/N Ratio |
---|
Level | S | F | D | R | S | F | D | R |
1 | 44.54 | 45.94 | - | - | −32.73 | −33.05 | −30.42 | −30.42 |
2 | 33.41 | 32.99 | - | - | −30.23 | −30.18 | −30.42 | −30.42 |
3 | 26.73 * | 25.75 * | - | | −28.29 * | −28.02 * | −30.42 | |
Delta | 17.82 | 20.19 | - | - | 4.44 | 5.03 | 0.00 | 0.00 |
Rank | 2 | 1 | 3 | 4 | 2 | 1 | 3 | 4 |
Table 9.
Analysis of variance for Ra.
Source | DF | Adj SS | Adj MS | F-Value | p-Value | Contribution (%) |
---|
S | 2 | 0.000721 | 0.000360 | 60.07 | 0.091 | 19.32 |
F | 2 | 0.000048 | 0.000024 | 4.02 | 0.333 | 1.29 |
D | 2 | 0.002918 | 0.001459 | 243.19 | 0.045 | 78.21 |
R | 1 | 0.000038 | 0.000038 | 6.26 | 0.242 | 1.02 |
Error | 1 | 0.000006 | 0.000006 | - | - | 0.16 |
Total | 8 | 0.003731 | - | - | - | 100 |
Table 10.
Analysis of variance for VB.
Source | DF | Adj SS | Adj MS | F-Value | p-Value | Contribution (%) |
---|
S | 2 | 3249.56 | 1624.78 | 1083.19 | 0.021 | 82.19 |
F | 2 | 246.22 | 123.11 | 82.07 | 0.078 | 6.23 |
D | 2 | 262.89 | 131.44 | 87.63 | 0.075 | 6.65 |
R | 1 | 193.39 | 193.39 | 128.93 | 0.056 | 4.89 |
Error | 1 | 1.50 | 1.50 | | - | 0.04 |
Total | 8 | 3953.56 | - | - | - | 100 |
Table 11.
Analysis of variance for MRR.
Source | DF | Adj SS | Adj MS | F-Value | p-Value | Contribution (%) |
---|
S | 2 | 496,963 | 248,481 | 1.39 | 0.419 | 5.91 |
F | 2 | 761,419 | 380,709 | 2.13 | 0.32 | 9.05 |
D | 2 | 6,795,563 | 3,397,781 | 18.98 | 0.05 | 80.78 |
Error | 2 | 358,112 | 179,056 | | | 4.26 |
Total | 8 | 8,412,056 | | | | 100.00 |
Table 12.
Analysis of variance for CT.
Source | DF | Adj SS | Adj MS | F-Value | p-Value | Contribution (%) |
---|
S | 2 | 486.08 | 243.041 | 34.98 | 0.003 | 42.58 |
F | 2 | 627.68 | 313.84 | 45.17 | 0.002 | 54.98 |
Error | 4 | 27.79 | 6.948 | - | - | 2.43 |
Total | 8 | 1141.55 | - | - | - | 100 |
Table 13.
The predicted and confirmed values at single optimal setting.
Machining Characteristic | Optimal Parameter Combination | Optimal Predicted Values | Experimental Values | Prediction Error (%) |
---|
Surface roughness, µm | S3F1D1R2 | 0.169 | 0.167 | 1.18 |
Tool wear, µm | S1F3D1R2 | 43.67 | 44.65 | 2.24 |
Cutting time, s | S3F3 | 19.72 | 19.72 | 0 |
Material removal rate, mm3/min | S3F3D3 | 4550 | 4550 | 0 |
Table 14.
Normalized values and deviation sequences of machinability characteristics.
Exp. No | S/N Ratio | Normalized Values | Deviation Sequences |
---|
Ra | VB | CT | MRR | Ra | VB | CT | MRR | Ra | VB | CT | MRR |
---|
1 | 15.060 | −35.707 | −35.364 | 63.046 | 0.407 | 0.000 | 1.000 | 0.000 | 0.593 | 1.000 | 0.000 | 1.000 |
2 | 13.660 | −36.258 | −32.490 | 65.296 | 0.829 | 0.103 | 0.696 | 0.642 | 0.171 | 0.897 | 0.304 | 0.358 |
3 | 12.439 | −36.902 | −30.336 | 67.959 | 1.000 | 0.152 | 0.469 | 0.982 | 0.000 | 0.848 | 0.531 | 0.018 |
4 | 14.494 | −39.085 | −32.865 | 64.629 | 0.407 | 0.631 | 0.736 | 0.622 | 0.593 | 0.369 | 0.264 | 0.378 |
5 | 13.159 | −39.825 | −29.991 | 66.880 | 0.770 | 0.769 | 0.432 | 1.000 | 0.230 | 0.231 | 0.568 | 0.000 |
6 | 14.457 | −40.906 | −27.836 | 69.542 | 0.075 | 0.052 | 0.205 | 0.389 | 0.925 | 0.948 | 0.795 | 0.611 |
7 | 13.351 | −41.727 | −30.928 | 65.968 | 0.617 | 0.971 | 0.531 | 0.952 | 0.383 | 0.029 | 0.469 | 0.048 |
8 | 15.376 | −42.345 | −28.052 | 68.219 | 0.000 | 1.000 | 0.228 | 0.378 | 1.000 | 0.000 | 0.772 | 0.622 |
9 | 13.906 | −41.938 | −25.898 | 70.881 | 0.357 | 0.927 | 0.000 | 0.982 | 0.643 | 0.073 | 1.000 | 0.018 |
Table 15.
Grey relational coefficients (GRCs) and GRG.
Exp. No | GRC | GRG | Rank |
---|
Ra | VB | CT | MRR |
---|
1 | 0.458 | 0.333 | 1.000 | 0.333 | 0.520 | 8 |
2 | 0.745 | 0.358 | 0.622 | 0.582 | 0.547 | 6 |
3 | 1.000 | 0.371 | 0.485 | 0.966 | 0.705 | 3 |
4 | 0.458 | 0.575 | 0.654 | 0.570 | 0.569 | 5 |
5 | 0.684 | 0.684 | 0.468 | 1.000 | 0.713 | 2 |
6 | 0.351 | 0.000 | 0.386 | 0.450 | 0.292 | 9 |
7 | 0.566 | 0.945 | 0.516 | 0.912 | 0.732 | 1 |
8 | 0.333 | 1.000 | 0.393 | 0.446 | 0.547 | 7 |
9 | 0.437 | 0.872 | 0.333 | 0.966 | 0.657 | 4 |
Table 16.
Response table for grey relational grade for “larger-the-better”.
Factors | Mean of Means |
---|
Level | S | F | D | R |
1 | 0.5909 | 0.6070 * | 0.4531 | 0.6185 * |
2 | 0.5248 | 0.6025 | 0.5909 | 0.5239 |
3 | 0.6453 * | 0.5515 | 0.7169 * | |
Delta | 0.1206 | 0.0555 | 0.2638 | 0.0946 |
Rank | 2 | 4 | 1 | 3 |
Table 17.
Analysis of variance for GRG.
Source | DF | Adj SS | Adj MS | F-Value | p-Value | Contribution (%) |
---|
V | 2 | 0.021873 | 0.010936 | 13.99 | 0.186 | 14.52 |
F | 2 | 0.005706 | 0.002853 | 3.65 | 0.347 | 3.79 |
D | 2 | 0.104428 | 0.052214 | 66.80 | 0.086 | 69.30 |
R | 1 | 0.017892 | 0.017892 | 22.89 | 0.131 | 11.87 |
Error | 1 | 0.000782 | 0.000782 | - | - | 0.52 |
Total | 8 | 0.150681 | - | - | - | 100.00 |
Table 18.
Confirmation results considering initial and optimal parameters of GRG.
Characteristic | Initial Parameter Setting (Random) (Order No. 4) | Optimal Parameter Setting |
---|
Initial Best Parameters Taguchi–GRA (Order No. 7) | Predicted Optimal Parameters |
---|
Prediction | Experiment |
---|
Factor levels | S2F1D2R3 | S3F1D3R2 | S3F1D3R1 | S3 F1D3R1 |
Ra (µm) | 0.198 | 0.208 | - | 0.182 |
MRR (mm3/min) | 1224 | 2550 | - | 2550 |
VB (µm) | 90 | 111 | - | 101 |
CT (s) | 43.98 | 35.19 | | |
GRG | 0.569 | 0.732 | 0.794 | - |
Improvement in GRG | 0.225 | 0.062 | |
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