Document Type : Research Article
Authors
^{1} Department of Mechanical Engineering, IMPACT College of Engineering & Applied Sciences, Sahakaranagar South, Kodigenhali, Bangaluru 560092, Karnataka, India.
^{2} Department of Mechanical Engineering St. Joseph’s College of Engineering & Technology, Choondacherry, Kottayam, 686579, Kerala, India
^{3} Department of Mechanical Engineering, CVR College of Engineering, Ibrahimpatnam, Hyderabad 501510, Telangana, India
^{4} Department of Mechanical Engineering, Gurunanak Institutions Technical Campus, Ibrahimpatnam, Hyderabad, 501506 Telangana, India
Abstract
Keywords
Main Subjects
Research Article
Jalumedi Babu^{ a*} , Lijo Paul ^{b}, Maringanti Venkata Ramana ^{c}, Anjaiah Madarapu^{ d}
^{a }Department of Mechanical Engineering, IMPACT College of Engineering & Applied Sciences, Sahakaranagar South,
Kodigenhali, Bangaluru 560092, Karnataka, India.
^{b}^{ }Department of Mechanical Engineering St. Joseph’s College of Engineering & Technology, Choondacherry, Kottayam,
686579, Kerala, India
^{C} Department of Mechanical Engineering, CVR College of Engineering, Ibrahimpatnam, Hyderabad 501510, Telangana, India
^{d} Department of Mechanical Engineering, Gurunanak Institutions Technical Campus, Ibrahimpatnam, Hyderabad, 501506 Telangana, India
ARTICLE INFO 

ABSTRACT 
Article history: Received: 20230916 Revised: 20240318 Accepted: 20240325 

Glassfiberreinforced polymers' (GFRP), as compared to metallic materials, require more intricate machining. The composite construction experiences delamination as a result of this machining operation. Delamination at the exit and entrance of holes drilled is a significant flaw in composite materials. Superiordrilled holes can be produced by optimizing the drilling process's governing factors. This study’s goal is to maximize the drilling settings using entropy weightcoupled gray relational analysis with fuzzy logic to account for multiple performance factors. Taguchi's L25 5level orthogonal array is used to increase the accuracy of the results in this study. Feed rate and spindle speed are considered the control variables, and torque, thrust force, and delamination at both the exit and entry are the responses. The results show that drilling performance is enhanced by lower feed rates and elevated spindle speeds. Additionally, the present findings show that feed rate has a stronger influence on drilling hole quality. These results also proved that increasing the number of levels increases the accuracy of the results. Entropybased gray relational analysis with fuzzy logic using more levels of factors can be effectively used for the optimization of the drilling process. 



Keywords: Composites; Delamination; Equivalent delamination factor; Grey relational analysis; Entropy; Fuzzy logics. 


© 2024 The Author(s). Mechanics of Advanced Composite Structures published by Semnan University Press. This is an open access article under the CCBY 4.0 license. (https://creativecommons.org/licenses/by/4.0/) 
In industries like the production of automobiles, defense equipment, and airplanes, where the need for structures with low weight, high strength, and stiffness is crucial, designers often turn to composites as an alternative to standard metallic materials [1]. These materials are challenging to machine due to their innate characteristics, such as high heterogeneity and abrasive structure, low thermal conductivity, and heat sensitivity. These materials exhibit a variety of flaws throughout the machining process, including matrix cracking, deboning, and delamination [2–4]. Most scientists who studied the drilling GFRP composite concentrated on thrust force and its influence on machining damages, in particular delamination. A detailed discussion on delamination and the techniques of evaluation and measurement were provided elsewhere [5, 6].
The impact of machining parameters while machining GFRP composites was studied by Khashaba and his colleagues both empirically and analytically, with an emphasis on delamination and thrust force [7]. Formisano et al. [8] looked into how production processes affected the mechanical properties of GFRP composite laminates. The effects of drilling conditions, such as spindle speed, feed rate, and drill bits, on the delamination and temperature of GFRP composite laminates were examined by Erturk et al. [9]. In order to decrease delamination and enhance hole quality, recent research has focused on the geometry and coatings of drill bits [10–12]. A few investigations concentrated on the impact of tool wear [13] as well as exit temperatures [14–18] on delamination and surface degradation.
The prediction of thrust forces because of tool wear during drilling CFRP/Al stack [19] and CFRP [20] unidirectional composites was another recent study's main focus. A thorough analysis of delamination and delaminationfree machining techniques for CFRP composites was presented by Jai et al. [21, 22]. Rahmé et al.'s research [22] demonstrated that the addition of woven glass sheets to the CFRP sheets' exit side of the drilled hole helped reduce delamination. Galinska et al. [23] provided a thorough analysis of bolted joints used to link fiberreinforced composites. The use of unconventional methods to minimize delamination damage during the drilling of composites was the subject of several studies [17, 24].
For thrust forces and delamination damage, the drill bit tip angle is thought to be a key influencing factor. Improper cuttingedge design results in unintended cutting angles being distributed, which leads to poor quality and ineffective cutting ability, which leads to increased thrust forces and delamination [25, 26].
Arrospide et al. [27] looked into the impact of various drill bit geometries on the diameter deviation, surface roughness, and coaxial aspects of hole quality. Liu et al.'s experiments [28] show that thrust forces built by extruding the chisel edge were greater than those produced by cutting the chisel edge. According to Qiu et al. [29], milling CFRP laminates with a compounded drill, dragger drill, or candlestick drill could minimize or completely prevent pushout delamination. Investigations by Hocheng et al. with various drill bits like twist drill, candle stick drill, saw drill, core drill, and step drill concluded that the core drill allows the grater critical feed; below this force, delamination will not occur [30].
According to different delamination factor models, such as the conventional delamination factor, adjusted delamination factor, and equivalent delamination factor, Keerthy & J. Babu [7] studied the influence of speed along with feed on delamination at the exit side of the drilled hole in GFRP composites. The findings showed that feed has a greater impact on pushout delamination. To demonstrate a relationship between speed and feedon delamination in a composite lamina, Davim and Reis provided a method employing Taguchi's method and ANOVA [8]. Using the Taguchi method with Grey Relational Analysis, Palanikumar suggested an efficient procedure for optimizing drilling conditions (feed and speed) with several performance characteristics (surface roughness, thrust force, and delamination factor). Their research outcome suggests that feed has a larger impact compared to spindle speed [7].
The majority of researchers used Taguchi and ANOVA methodologies to conduct their experiments with 3 or 4 levels to calculate the impact of drilling factors on delamination during drilling composite laminate [6–10]. In variation with past research, the Taguchi L25, a 5level orthogonal array, was used in the experiments in the current work, which is expected to boost the accuracy of the findings. Feed and speed are the control variables considered in this investigation. The major goal of this work is to use the Taguchi technique and hybrid optimization method. The entropy method was used to calculate weights, which are integrated with grey relational analysis along with fuzzy logic to optimize the drilling conditions during the drilling of GFRP composite by a diamondcoated core drill, which allows a larger critical thrust force while drilling.
The most promising equivalent delamination factor was applied to assess the delamination damage affecting composite laminate near the exit and entrance of the hole, which further improves the accuracy of the results. MINITAB 17 was used for the design and analysis of drilling experiments to determine the significant variables that influence the drilling of GFRP composites.
The research questions of this study are: what is the optimum machining factor for minimizing drilling defects, and which is the most influential factor on drilling performance? Selection of a suitable MCDM method to obtain the optimum machining combination.
Updates and improvements are still being made to MCDM approaches. By using the MCDM methodology, the shortcomings of more solitary approaches are mitigated. For example, all evaluation criteria and subcriteria should stand alone when using the analytical hierarchy process (AHP) approach. Nonetheless, certain criteria (or subcriteria) are dependent on other criteria in a lot of realworld working situations. The analytic network process (ANP) method overcomes this drawback of the AHP method. This approach considers the interdependencies among the criteria [31, 32]. The VIKOR method could resolve decision problems with conflicting and noncommensurable criteria, but it has limitations, like a lack of flexibility. The Complex Proportional Assessment Method (COPRAS) has advantages as it takes both maximizing and minimizing criteria values into account with different methods; however, it has disadvantages as the ranking derived from the COPRAS method is unstable compared to the other MCDM methods [31, 32].
The multiattributive border approximation area comparison (MABAC) approach and its extensions have demonstrated strong results in a number of application domains. Three primary benefits are offered by MABAC: stable solutions in the event that the type of criteria formulation changes, consistent results in the event that the units of measurement vary, and a streamlined algorithm appropriate for largescale issues. Though MABAC has structural constraints, it can still be enhanced. The normalizing method used in the classic MABAC is based on a maxmin normalization formula, which is one of its major flaws. One normalizing method alone, meanwhile, could produce skewed results [33].
The MultiAtributive IdealReal Comparative Analysis (MAIRCA) method has the following advantages: this method has a mathematical framework that remains the same regardless of the number of alternatives and criteria, hence the possibility of MAIRCA application in cases of a large number of alternatives and criteria. This method has applicability to both qualitative and quantitative criteria types. This method gives stable solutions regardless of changes in the qualitative criteria measurement scale and changes in quantitative criteria formulation [34]. The MAIRCA method can solve the problems under uncertainty. It is an efficient tool that emphasizes the importance of qualitative criteria in realtime problemsolving. Rating the qualitative criteria using an arbitrary scale merely for comparison purposes can yield incorrect results. Therefore, the tool is equipped with experimentally available or statistically evaluated material data along with the opinions of the subject experts to accurately assess the candidate choices in a given engineering problem [35].
The abovementioned method has its relative advantages and limitations. The present study uses Grey Relational Analysis (GRA). The reason for using GRA is to reduce uncertainty in decisionmaking processes by providing a quantitative measure of the relationship between different factors. GRA is particularly useful when dealing with small sample sizes or data. It is also effective in situations where there is a lack of complete information about the variables being analyzed. Recent research shows GRA, along with fuzzy logic, can be effectively used for different multicriteria decisionmaking applications [36–38]. The present study uses the same method for optimizing the machining factors during the drilling of GFRP composite laminate.
The pairwise comparison and deviation from maximum consistency concepts are applied in the comparisonbased MCDM process known as the full consistency technique (FUCOM). Just n − 1 pairwise comparisons are needed by FUCOM to assign weights to n mappable targeting criteria in MPM. The FUCOM results are validated using the comparisons' deviation from maximum consistency (DMC). The FUCOM weighting method, as compared to other methodologies, yields more trustworthy results because it makes the fewest potential comparisons in its theory. The most significant shortcoming of FUCOM has been considered to be its subjectivity [39, 40].
A subjective weighing technique called Level Based Weight Assessment (LBWA) is suggested as a solution to pairwise comparison problems. In comparison to both the BWM and AHP approaches, it is based on a (n1) comparison. One of the main advantages of the LBWA approach is its capacity to maintain its basic structure regardless of how complex the model gets. Furthermore, the ideal values of weight coefficients are obtained by a straightforward mathematical apparatus, which eliminates the conflicting expert preferences allowed by other subjective models like BWM and AHP. Finally, sensitivity analysis of the MCDM mode is made possible by the elasticity coefficient of the LBWA model, which permits extra coefficient corrections based on the preferences of decisionmakers [41].
Unlike the above subjective methods, objective methods do not require any sort of initial information or judgment from the decisionmakers [42]; they merely assess the structure of the data available in the decision matrix to determine the weights. These methods are known for eliminating possible bias associated with subjective evaluation, thus increasing objectivity. Criteria Importance Through Intercriteria Correlation (CRITIC) has an advantage, as it considers both the contrast intensity and the conflicting relationship held by each decision criterion [43, 44].
Ecer and Pamucar [45] recently introduced an objective weighting method named Logarithmic Percentage changedriven Objective Weighting (LOPCOW) with the advantages of eliminating the gap due to the size of the data, generating more reasonable weightings, and considering both positive and negative data in the weighting process. Famucar et.al. [46] proposed a novel multicriteria decision support tool called Weights by ENvelope and SLOpe (WENSLO) and AczelAlsina Weighted ASsessment (ALWAS) to identify the green growth performance of countries.
By removing the impact of human variables on criteria weights, the entropy technique has the advantage of improving the evaluation results' objectivity and scientificity [37]. As per the review on the benefits of the entropy weight method (ewm), it has the following benefits in optimizing the machining process [47]. One very effective method for evaluating indications is the EWM weight calculation process. This method is proven to be sufficiently consistent in determining the combined contrast intensity and divergence of responses, as well as inappropriately allocating weights to them [37, 47].
From the above discussion, entropy weightbased gray relational analysis with fuzzy logic can be effectively used for multicriteria decisionmaking processes. The present study aims to use the same for determining the optimum drilling conditions during the drilling of composite laminate. The methodology used in this study is shown in Fig. 1.
Fig. 1. Methodology used in this study
In this investigation, 26layer GFRP composite laminates that were set up symmetrically in the form [0, 90] were utilized. Bidirectional EGlass fibers were used, and grade L12 resin with K5 hardener was used as the applied resin. The laminate had a 6 mm thickness. A laminate was cut to the workpiece material sample size of 250 x 40 x 6 mm^{3}. Drilling experiments were carried out using a 10 mm diamondcoated core drill on GFRP laminates in accordance with Taguchi's L25 orthogonal array. Experiments were done using a CNC computer numerical control vertical machining center (Makino Vertical Machining Centre, Model S33) at PSG College of Engineering in Coimbatore, India. To reduce experimental error, each experiment was run twice.
Figure 2 depicts the experimental setup with the dynamometer. The strain gauge theory underlies how the dynamometer operates. The torque and thrust force values that generate voltage are proportionate to the force applied, and torque is responsible for the Wheatstone bridge circuit imbalance. The force and torque fluctuations while drilling were captured and then stored with a digital storage oscilloscope (Tektronix TDS210). The trials also took pushout and peelup delamination effects into account. No coolant was applied during any of the testing. The drilling conditions considered for this investigation are shown in Table 1.
Fig. 2. Drilling setup with dynamometer and digital display
Table 1. Drilling conditions with their levels
Level of parameters 
Speed (rpm) 
Feed (mm/min) 
1 
1500 
50 
2 
1750 
75 
3 
2000 
100 
4 
2250 
125 
5 
2500 
150 
Different researchers have used a variety of techniques to assess the delamination of composites caused by drilling, although Xray [12], optical microscope [7–9], ultrasonic Cscan [13], and digital photography [16] are the most popular. Acoustic emission [15] and the shadow Moire laserbased imaging technology [16] are other delamination measurement techniques. Babu et al. [5] give a thorough analysis of the assessment methods of delamination in a review paper.
In this investigation, the delamination damage at the entrance and exit of the drilled hole was determined using digital image processing technologies. A scanner with a resolution of 1200 dpi was used to scan these drilled holes in order to calculate the amount of delamination. The imageediting application Image J received the scanned images and imported them.
A number of parameters, including brightness intensity, image enhancement, noise suppression, and edge detection, which are discussed in more depth elsewhere [48, 49], must be carefully chosen in order to produce a picture of acceptable quality. The threshold filter was applied to the binary image to remove the black and gray points, and only then can the damage zone be measured. Figure 3 illustrates the image processing procedure followed for obtaining the delaminated area of the drilled hole with acceptable quality.
Fig. 3. Image processing steps to assess delamination damage
The damage intensity to the composite material at the exit and entry sides of the hole is characterized in the present investigation using the equivalent delamination factor, which is schematically represented in Fig. 4 and computed using Eq. (1).
Fig. 4. Schematic for calculation of equivalent
delamination factor

(1) 
here D_{o} is the diameter of the nominal hole. De is the equivalent delamination diameter which may be expressed as Eq. (2).

(2) 
A_{d} = the delamination damage area in the surroundings of the drilled hole.
A_{o} = the drilled area with diameter D_{o}.
Responses from the experiments are delaminations, both pushout and peelup, torque and thrust force for various drilling conditions, as shown in Table 2.
Due to their excellent mechanical qualities, GFRP composites are employed in fairings, storage room doors, passenger compartments, and wind turbine blades. Prior to assembly, drilling is a typical machining procedure on these pieces. Drilling without errors is necessary to guarantee their effective operation in service. The literature on drilling GFRP composites reveals that because these materials have a composite structure containing hard fibers in a soft matrix, their machining mechanisms differ from those of traditional metals. These materials can be machined through shearing or plastic deformation. The process of machining these composite materials was affected by the fibers' hardness, toughness, orientation, and flexibility [9]. For these composite materials, it is particularly challenging to optimize many features simultaneously. In the current work, drilling process parameters for GFRP composites are optimized for numerous performance factors. Performance parameters of drilling include thrust and torque, as well as delamination at both the entry and exit. For better hole quality, lower torque, delamination factor, and thrust force values are preferred. The feed rate and spindle speed input parameters. Using response graphs, the influence of these variables on the machining of GFRP composites is studied.
Table 2. Orthogonal array of experimental design with variable and experiment responses

Speed (rpm) 
Feed (mm/min) 
Delamination Factor 
Thrust Force (N) 
Torque (Nm) 

Exp. No 
Pushout 
Peelup 

1 
1500 
50 
1.15 
1.14 
143.50 
0.48 
2 
1500 
75 
1.17 
1.14 
246.00 
0.77 
3 
1500 
100 
1.19 
1.15 
398.50 
1.06 
4 
1500 
125 
1.21 
1.15 
522.50 
1.30 
5 
1500 
150 
1.21 
1.16 
680.50 
1.60 
6 
1750 
50 
1.14 
1.14 
103.00 
0.44 
7 
1750 
75 
1.15 
1.14 
220.00 
0.73 
8 
1750 
100 
1.16 
1.15 
334.00 
0.99 
9 
1750 
125 
1.17 
1.15 
455.50 
1.18 
10 
1750 
150 
1.21 
1.15 
586.00 
1.44 
11 
2000 
50 
1.14 
1.13 
108.50 
0.45 
12 
2000 
75 
1.14 
1.14 
203.00 
0.67 
13 
2000 
100 
1.15 
1.14 
308.00 
0.91 
14 
2000 
125 
1.16 
1.15 
406.50 
1.08 
15 
2000 
150 
1.20 
1.15 
487.50 
1.24 
16 
2250 
50 
1.12 
1.12 
67.00 
0.35 
17 
2250 
75 
1.14 
1.14 
94.50 
0.48 
18 
2250 
100 
1.14 
1.14 
145.50 
0.47 
19 
2250 
125 
1.15 
1.14 
209.50 
0.66 
20 
2250 
150 
1.18 
1.15 
255.00 
0.80 
21 
2500 
50 
1.13 
1.11 
61.50 
0.20 
22 
2500 
75 
1.15 
1.12 
96.50 
0.32 
23 
2500 
100 
1.16 
1.13 
136.50 
0.57 
24 
2500 
125 
1.16 
1.14 
180.50 
0.61 
25 
2500 
150 
1.19 
1.14 
246.00 
0.79 
A response table of average responses was used to construct the response graphs. Table 3 displays the response table with torque, delamination factors (entry and exit), and thrust force. ''Delta'' in the response table denotes the variation between the response's minimum and maximum average values at a specific level. The rank denotes the strength of a parameter's influence. According to the analysis of this response table, feed has a greater impact on the drilling of GFRP composites' output characteristics.
Table 3. Response table for thrust force, torque, peelup, and pushout delamination
Level 
Thrust force 
Torque 
Peelup delamination 
Pushout delamination 

Spindle 
Feed 
Spindle speed 
Feed 
Spindle speed 
Feed 
Spindle 
Feed 

1 
398.2 
96.7 
1.041 
0.380 
1.188 
1.135 
1.147 
1.129 

2 
339.7 
172.0 
0.951 
0.591 
1.167 
1.152 
1.144 
1.136 

3 
302.7 
264.5 
0.867 
0.797 
1.156 
1.160 
1.142 
1.141 

4 
154.3 
354.9 
0.549 
0.967 
1.148 
1.171 
1.138 
1.145 

5 
144.2 
451.0 
0.495 
1.172 
1.156 
1.197 
1.129 
1.149 

Delta 
254 
354.3 
0.546 
0.792 
0.040 
0.062 
0.018 
0.020 

Rank 
2 
1 
2 
1 
2 
1 
2 
1 

Fig. 5. S/N graphs for responses
Figures. 5 (a) to 5 (d) show the S/N curves for thrust force, torque, and delamination factors. The influence of speed and feed on torque and thrust force during drilling is depicted in Figs. 5 (a) and 5 (b). The findings show that when speed increases, torque and thrust force decrease. This occurs because increasing speed leads to more accumulated heat that softens the polymer matrix, resulting in reduced thrust force and torque. The stress on the drill, however, rises as the feed increases. When drilling composites, this results in increased torque and thrust force values. Figs. 5 (c) and 5 (d) show how drilling parameters affect the delamination damage at the exit and entry. High feed rates with low spindle speeds are more conducive to the delamination factor being seen. The delamination damage and thrust force increase with an increase in feed. Delamination and thrust force are related phenomena; when thrust force increases, the delamination also rises, and vice versa. Numerous scholars have examined the features of individual performance [8–12]. To boost production and enhance the performance of manufactured components, it is required to optimize several performance attributes. Researchers employ a variety of strategies to optimize several performance parameters, including the utility concept, gray relational analysis [49], and desirability approach [50]. In variation with past research, in this study, GreyEntropyFuzzy (GEF), a hybrid method was employed in order to get the best drilling conditions for these multiple response optimizations. This is a mix of fuzzy logic with gray relational analysis [51, 52], and response weights were determined using the entropy approach.
The drilling issue that occurred during the drilling of GFRP laminate was optimized using GRA (greyrelational analysis). GRA is a quantitative technique for identifying disparity and equality among input conditions. Every output response has a unique range and unit. Hence, it is necessary to normalize these values between 0 and 1. When solving problems involving several objectives, certain responses could be considered as maximization, some responses as minimization, and some responses as nominal, which are better responses. GRA condenses multiresponse issues into a single response known as the Grey Relational Coefficient.
Responses with maximization can be normalized by utilizing Eq. (3).

(3) 
Responses of minimization are normalized by using Eq. (4).

(4) 
Responses with nominal values the better can be normalized by using Eq. (5).

(5) 
i= 1 to n, n = number of drilling conditions
m = number of experimental data
is the original sequence
is the sequence after data preprocessing the max is greatest value in ,
min = least value in
= desired value.
In this investigation, all output responses are lower the better performance characteristic type, Eq. (4) is used to obtain the normalized values.
Normalized values for all the responses are calculated and tabulated in Table 5.
Now Grey Relational Coefficients were determined by using Eq. (6).

(6) 
, , are determined using the Eq.’s (7), (8) and (9):

(7) 

(8) 

(9) 
ζ is the coefficient, whose values range [0,1].
ζ = 0.5 is generally used.
=deviation sequence of the sequence
=comparability sequence.
The deviation sequences of the responses were calculated after data preprocessing and are shown in Table 4. The values and can be found in Table 4.
GRCs calculated with Eq. (6) for drilling conditions are represented in Table 4. Notations used for output responses are,
According to Eq. (10), the grey relational grade is often determined as the mean of all the GRCs of the relevant responses. Only when each response is given the same weight can this equation be used:
(k) 
(10) 
For experimental problems such as drilling all output responses may not be equally significant, hence by assigning different weights to the responses, then Eq. (10) may be modified as Eq. (11).

(11) 
where is the normalized weight of the response k; when weights are the same Eq. (10) and (11) both are the same. In the present study an objective method, that is entropy method_{ }[24,25] was used for the determination of criteria weights of output responses.
Table 4. Normalized and Deviation sequences of output responses.
Experiment 
Normalized Values 

Deviation Sequence 

A 
B 
C 
D 
A 
B 
C 
D 

1 
0.353 
0.423 
0.680 
0.352 

0.648 
0.577 
0.321 
0.648 
2 
0.577 
0.653 
0.703 
0.585 

0.423 
0.348 
0.297 
0.415 
3 
0.777 
0.804 
0.764 
0.807 

0.223 
0.196 
0.236 
0.193 
4 
0.890 
0.901 
0.831 
0.970 

0.110 
0.099 
0.169 
0.030 
5 
1.000 
1.000 
1.000 
1.000 

0.000 
0.000 
0.000 
0.000 
6 
0.215 
0.381 
0.565 
0.270 

0.786 
0.619 
0.435 
0.730 
7 
0.530 
0.624 
0.674 
0.392 

0.470 
0.376 
0.326 
0.608 
8 
0.704 
0.770 
0.760 
0.419 

0.296 
0.231 
0.240 
0.581 
9 
0.833 
0.853 
0.820 
0.567 

0.167 
0.147 
0.180 
0.433 
10 
0.938 
0.948 
0.903 
0.981 

0.062 
0.052 
0.098 
0.019 
11 
0.236 
0.392 
0.522 
0.194 

0.764 
0.608 
0.478 
0.806 
12 
0.497 
0.583 
0.618 
0.293 

0.503 
0.417 
0.382 
0.707 
13 
0.670 
0.729 
0.722 
0.338 

0.330 
0.271 
0.278 
0.662 
14 
0.786 
0.813 
0.803 
0.426 

0.214 
0.187 
0.197 
0.574 
15 
0.861 
0.879 
0.837 
0.816 

0.139 
0.121 
0.164 
0.184 
16 
0.036 
0.278 
0.337 
0.000 

0.964 
0.722 
0.664 
1.000 
17 
0.179 
0.423 
0.565 
0.232 

0.821 
0.577 
0.435 
0.768 
18 
0.358 
0.413 
0.663 
0.286 

0.642 
0.587 
0.337 
0.714 
19 
0.510 
0.576 
0.747 
0.398 

0.490 
0.424 
0.254 
0.602 
20 
0.592 
0.671 
0.776 
0.696 

0.408 
0.329 
0.224 
0.304 
21 
0.000 
0.000 
0.000 
0.123 

1.000 
1.000 
1.000 
0.877 
22 
0.187 
0.235 
0.329 
0.358 

0.813 
0.765 
0.671 
0.642 
23 
0.332 
0.510 
0.447 
0.431 

0.668 
0.490 
0.553 
0.569 
24 
0.448 
0.538 
0.618 
0.473 

0.552 
0.462 
0.382 
0.527 
25 
0.577 
0.662 
0.740 
0.733 

0.423 
0.338 
0.260 
0.267 
Entropy, which is an estimate when there is uncertainty in information or data, was proposed by Shanon and Weaver in 1947. Zeleney improved it further in 1982 for determining the objective weights of responses. It applies the theory of probability. The weights of responses by this method can be calculated by normalizing the data with Eqs. (2) and (3). The values of entropy for individual output responses are determined using Eq. (12).

(12) 
here and m=total no of experimental conditions, in present study m=25.
The performance response or characteristics is increasing or decreasing with entropy values. The weights of the individual responses may be determined by Eq. (13).

(13) 
Calculated normalized values of responses are tabulated in Table 5.
Using these entropy values and also weights for the responses, they are calculated using Eqs. (12) and (13) respectively, which are presented in Table 6.
Table 5. Normalized, values for output responses
Experiment 
Normalized Values 
Values 
Values 

A 
B 
C 
D 
A 
B 
C 
D 
A 
B 
C 
D 

1 
0.8676 
0.8133 
0.5000 
0.7000 
0.0520 
0.0533 
0.0405 
0.0490 
0.154 
0.156 
0.130 
0.148 

2 
0.7022 
0.6200 
0.5000 
0.5000 
0.0421 
0.0406 
0.0405 
0.0350 
0.133 
0.130 
0.130 
0.117 

3 
0.4560 
0.4267 
0.3333 
0.3000 
0.0273 
0.0279 
0.0270 
0.0210 
0.098 
0.100 
0.098 
0.081 

4 
0.2559 
0.2667 
0.3333 
0.1000 
0.0153 
0.0175 
0.0270 
0.0070 
0.064 
0.071 
0.098 
0.035 

5 
0.0008 
0.0667 
0.1667 
0.1000 
0.0000 
0.0044 
0.0135 
0.0070 
0.000 
0.024 
0.058 
0.035 

6 
0.9330 
0.8400 
0.5000 
0.8000 
0.0560 
0.0550 
0.0405 
0.0559 
0.161 
0.160 
0.130 
0.161 

7 
0.7441 
0.6467 
0.5000 
0.7000 
0.0446 
0.0423 
0.0405 
0.0490 
0.139 
0.134 
0.130 
0.148 

8 
0.5601 
0.4733 
0.3333 
0.6000 
0.0336 
0.0310 
0.0270 
0.0420 
0.114 
0.108 
0.098 
0.133 

9 
0.3640 
0.3467 
0.3333 
0.5000 
0.0218 
0.0227 
0.0270 
0.0350 
0.083 
0.086 
0.098 
0.117 

10 
0.1533 
0.1733 
0.3333 
0.1000 
0.0092 
0.0113 
0.0270 
0.0070 
0.043 
0.051 
0.098 
0.035 

11 
0.9241 
0.8333 
0.6667 
0.8000 
0.0554 
0.0546 
0.0541 
0.0559 
0.160 
0.159 
0.158 
0.161 

12 
0.7716 
0.6867 
0.5000 
0.8000 
0.0463 
0.0450 
0.0405 
0.0559 
0.142 
0.139 
0.130 
0.161 

13 
0.6021 
0.5267 
0.5000 
0.7000 
0.0361 
0.0345 
0.0405 
0.0490 
0.120 
0.116 
0.130 
0.148 

14 
0.4431 
0.4133 
0.3333 
0.6000 
0.0266 
0.0271 
0.0270 
0.0420 
0.096 
0.098 
0.098 
0.133 

15 
0.3123 
0.3067 
0.3333 
0.2000 
0.0187 
0.0201 
0.0270 
0.0140 
0.075 
0.078 
0.098 
0.060 

16 
0.9911 
0.9000 
0.8333 
1.0000 
0.0594 
0.0589 
0.0676 
0.0699 
0.168 
0.167 
0.182 
0.186 

17 
0.9467 
0.8133 
0.5000 
0.8000 
0.0568 
0.0533 
0.0405 
0.0559 
0.163 
0.156 
0.130 
0.161 

18 
0.8644 
0.8200 
0.5000 
0.8000 
0.0518 
0.0537 
0.0405 
0.0559 
0.153 
0.157 
0.130 
0.161 

19 
0.7611 
0.6933 
0.5000 
0.7000 
0.0456 
0.0454 
0.0405 
0.0490 
0.141 
0.140 
0.130 
0.148 

20 
0.6877 
0.6000 
0.3333 
0.4000 
0.0412 
0.0393 
0.0270 
0.0280 
0.131 
0.127 
0.098 
0.100 

21 
1.0000 
1.0000 
1.0000 
0.9000 
0.0600 
0.0655 
0.0811 
0.0629 
0.169 
0.178 
0.204 
0.174 

22 
0.9435 
0.9200 
0.8333 
0.7000 
0.0566 
0.0602 
0.0676 
0.0490 
0.163 
0.169 
0.182 
0.148 

23 
0.8789 
0.7533 
0.6667 
0.6000 
0.0527 
0.0493 
0.0541 
0.0420 
0.155 
0.148 
0.158 
0.133 

24 
0.8079 
0.7267 
0.5000 
0.6000 
0.0485 
0.0476 
0.0405 
0.0420 
0.147 
0.145 
0.130 
0.133 

25 
0.7022 
0.6067 
0.5000 
0.3000 
0.0421 
0.0397 
0.0405 
0.0210 
0.133 
0.128 
0.130 
0.081 

Sum of 
3.107 
3.126 
3.152 
3.098 
Entropy value for the response A is =  (3.107) =0.965.
Table 6. Weightages of the responses using
entropy method.
Response 



A 
0.965 
0.035 
28 
B 
0.971 
0.029 
24 
C 
0.979 
0.021 
17 
D 
0.962 
0.038 
31 
Sum 
0.123 
100 
The determined weights using Eq. (13) obtained for the responses are thrust force, torque, entry delamination factor, exit delamination factor, which are 0.28, 0.24, 0.17, and 0.31, respectively. These weights are used in determining the Grey relational grade with Eq. (11).
Table 7 represents the obtained GRCs, gray relation grades, and ranks for all the test runs.
Table 7. GRCs with the entropybased weights (in brackets), Grey Relational Grades and ranks for the test runs.
Experiment 
Grey Relational Coefficients 
Grey Relational Entropy Grade 
Rank 

Thrust Force 
Torque 
Peelup Delamination 
Pushout Delamination 

1 
0.5865 
0.5417 
0.4239 
0.5868 
0.5482 
8 
2 
0.4644 
0.4338 
0.4158 
0.4609 
0.4477 
15 
3 
0.3914 
0.3833 
0.3957 
0.3825 
0.3874 
21 
4 
0.3597 
0.3568 
0.3757 
0.3402 
0.3557 
23 
5 
0.3333 
0.3333 
0.3333 
0.33333 
0.3333 
25 
6 
0.6998 
0.5674 
0.4695 
0.6493 
0.6132 
6 
7 
0.4853 
0.4449 
0.4258 
0.5603 
0.4887 
13 
8 
0.4153 
0.3939 
0.3969 
0.5440 
0.4469 
16 
9 
0.3751 
0.3695 
0.3788 
0.4685 
0.4033 
20 
10 
0.3478 
0.3452 
0.3565 
0.3376 
0.3455 
24 
11 
0.6792 
0.5605 
0.4893 
0.7209 
0.6314 
4 
12 
0.5016 
0.4617 
0.4470 
0.6307 
0.5228 
10 
13 
0.4273 
0.4067 
0.4093 
0.5967 
0.4718 
14 
14 
0.3889 
0.3807 
0.3837 
0.5400 
0.4329 
17 
15 
0.3673 
0.3626 
0.3741 
0.3799 
0.3712 
22 
16 
0.9335 
0.6427 
0.5977 
1.0000 
0.8272 
2 
17 
0.7367 
0.5417 
0.4695 
0.6832 
0.6279 
5 
18 
0.5826 
0.5477 
0.4300 
0.6364 
0.5650 
7 
19 
0.4951 
0.4648 
0.4011 
0.5569 
0.4910 
12 
20 
0.4580 
0.4271 
0.3919 
0.4181 
0.4270 
19 
21 
1.0000 
1.0000 
1.0000 
0.8031 
0.9390 
1 
22 
0.7274 
0.6800 
0.6029 
0.5830 
0.6501 
3 
23 
0.6012 
0.4952 
0.5281 
0.5368 
0.5434 
9 
24 
0.5275 
0.4817 
0.4470 
0.5139 
0.4986 
11 
25 
0.4644 
0.4304 
0.4033 
0.4056 
0.4276 
18 
With grey relational analysis with entropybased weights, the grey relational entropy grade was determined. Experiment number 21 shows the greatest value of GREG, which represents the optimum values of input factors. The GREG values varied from 0.9390 to 0.3333. The experimental results of all output responses at optimized drilling conditions are entry delamination factor 1.13, exit delamination factor 1.11, thrust force 61.5 N, and torque 0.02 Nm.
Using GRA reduces ambiguity in decisionmaking processes by offering a numerical representation of the interplay between several components. When working with small sample sizes or lowquality data, GRA is especially helpful. A mathematical technique for expressing ambiguity and uncertainty in decisionmaking is fuzzy logic. It permits the possibility of partial truths, in which a claim may be made that is only partially true or untrue.
Fuzzy logic is based on the notion that there are frequently many shades of gray in between and that the concept of true or false is overly limiting. Hence, it is used to deal with imprecise or ambiguous information. Fuzzy rules, which are ifthen statements that represent the relationship between input and output variables in a fuzzy manner, are used to create fuzzy logic. A fuzzy set, or a set of membership degrees for every conceivable output value, is the result of a fuzzy logic system [53, 54]. Hence, in this study, grey relational analysis with fuzzy logic was used to optimize the drilling parameters.
Early optimization studies in the literature either employed subjected methods like the SIMO method or applied equal weights to all responses; this may be an inappropriate or incorrect method to optimize the drilling parameters. In order to make a multiobjective problem into a single objective known as GREG, the entropy approach, which is an objective method, was used combined with fuzzy logic to obtain the most scientific weights. Complex multiobjective optimization issues can be resolved by using a combination of grey relational analysis, the entropy method, and fuzzy logic [52]. However, relationships with assessing replies are disregarded during this conversion procedure. The improved optimization using the proper weights for each response is now presented by this approach.
In order to further optimize drilling using artificial intelligence techniques like fuzzy logic, a sound prediction model must be developed. Because GREG includes weighted sums that depend on entropy for each of the four GRCs, the GREG problem can be optimized without taking response criteria into consideration. For this, the GREG desirability function was applied with a fuzzy model for all input factors. The important phases of the fuzzy method are the fuzzification of the input and output data, the development of fuzzy rules, and eventually the defuzzification of outcomes.
The matching values of GEFG are obtained using the fuzzylogic toolbox of MATLAB (R2021a). Inputs to the fuzzylogic model are the values of the GREG of the torque, thrust force, exit and entry delamination, and diameter of the hole. The fuzzy modeling is done using triangular membership functions. Nine linguistic membership functions were used for all the input GREGs and output Grey Entropy Fuzzy Grade: lowest (LT), very low (VL), mediumlow (ML), low (L), mediumhigh (MH), high (H), medium higher (MHR), higher (HR), and highest (HT). In Fig. 6, these membership functions are shown. The obtained GEFG values are shown in Figs. 7 and 8, as displayed in the fuzzy rule viewer. In this figure, twentyfive rows show the fuzzy rules used, and the five columns represent GRC values, and the last column gives the defuzzified GEFG values. These GEFG values captured for all twentyfive experiments are shown in Table 8. It may be noted from Table 8 that the experiment. 21 (speed of 12000 rpm, feed of 1000 mm/min) has the greatest GEFG value; this indicates the optimum conditions of input variables for high drilling performance.
Fig. 6. Membership functions (a) for input factors and
(b) for output GEFG
Table 8. GRCs, GEG, and GEFG of all experiments
Experiment 
Grey Relational Coefficients 
Grey Relational 
Grey Entropy Fuzzy Grade 

Thrust Force 
Torque 
Peelup Delamination 
Pushout Delamination 

1 
0.5865 
0.5417 
0.4239 
0.5868 
0.5482 
0.500 
2 
0.4644 
0.4338 
0.4158 
0.4609 
0.4477 
0.434 
3 
0.3914 
0.3833 
0.3957 
0.3825 
0.3874 
0.385 
4 
0.3597 
0.3568 
0.3757 
0.3402 
0.3557 
0.375 
5 
0.3333 
0.3333 
0.3333 
0.33333 
0.3333 
0.375 
6 
0.6998 
0.5674 
0.4695 
0.6493 
0.6132 
0.618 
7 
0.4853 
0.4449 
0.4258 
0.5603 
0.4887 
0.442 
8 
0.4153 
0.3939 
0.3969 
0.5440 
0.4469 
0.423 
9 
0.3751 
0.3695 
0.3788 
0.4685 
0.4033 
0.375 
10 
0.3478 
0.3452 
0.3565 
0.3376 
0.3455 
0.375 
11 
0.6792 
0.5605 
0.4893 
0.7209 
0.6314 
0.670 
12 
0.5016 
0.4617 
0.4470 
0.6307 
0.5228 
0.500 
13 
0.4273 
0.4067 
0.4093 
0.5967 
0.4718 
0.462 
14 
0.3889 
0.3807 
0.3837 
0.5400 
0.4329 
0.419 
15 
0.3673 
0.3626 
0.3741 
0.3799 
0.3712 
0.375 
16 
0.9335 
0.6427 
0.5977 
1.0000 
0.8272 
0.925 
17 
0.7367 
0.5417 
0.4695 
0.6832 
0.6279 
0.673 
18 
0.5826 
0.5477 
0.4300 
0.6364 
0.5650 
0.500 
19 
0.4951 
0.4648 
0.4011 
0.5569 
0.4910 
0.455 
20 
0.4580 
0.4271 
0.3919 
0.4181 
0.4270 
0.424 
21 
1.0000 
1.0000 
1.0000 
0.8031 
0.9390 
0.952 
22 
0.7274 
0.6800 
0.6029 
0.5830 
0.6501 
0.714 
23 
0.6012 
0.4952 
0.5281 
0.5368 
0.5434 
0.500 
24 
0.5275 
0.4817 
0.4470 
0.5139 
0.4986 
0.469 
25 
0.4644 
0.4304 
0.4033 
0.4056 
0.5482 
0.415 
Fig. 7. Fuzzylogic rule viewer for Experiment number 21 (Greatest GEFG)
Fig. 8. Fuzzylogic rule viewer for Experiment number 5 (Least GEFG)
To more precisely find the optimum combinations of drilling parameters, it is still necessary to examine the relative importance of drilling factors for the different performance characteristics. The analysis of variance is used to analyze the outcomes. An analysis of variance (ANOVA) was utilized to determine which drilling variables have a substantial impact on performance characteristics. The complete variability of the Grey relationship grades is divided to achieve this. This is done in order to deconvolute the contributions made by individual drilling variables and errors from the total sum of the squared deviations of the Grey relational grade. To ascertain which machining factors significantly influence the drilling performance, the Ftest may also be performed. When F is large, changing the drilling parameter typically has a considerable impact on performance characteristics. The percentage of influence is also estimated for the analysis of the important variables and their contribution to composite machining. Table 9 displays these values.
Table 9. shows that the feed rate's F value is 26.34, which is higher than the spindle speed's 12.30 value. In light of this, and in good accord with results from Palanikumar [9], the feed rate is the variable that shows the most impact on torque, thrust force, and delamination variables while drilling GFRP laminate. The percentage error in the current study is 9.38, compared to 14.78 in a study of a similar nature by Palanikumar [9].
The employment of a larger number of levels is what accounts for the lower percentage error, or high accuracy, in the current work. Compared to Palanikumar's work, which only used 4 levels of input parameters, the current study uses 5.
Table 9. ANOVA for Grey Entropy Reasoning Grade
Source 
DF 
Sum of squares 
Mean square 
F 
% Contribution 
Speed (rpm) 
4 
0.14064 
0.035159 
12.30 
28.85 
Feed(mm/min) 
4 
0.30115 
0.075288 
26.34 
61.77 
Residual Error 
16 
0.04574 
0.002858 

9.38 
Total 
24 
0.48752 



Figure 9 shows how the parameters feed and speed interact to influence the drilling performance of GFRP composite laminate. If the lines are parallel, there is little interaction between the parameters. It will have an interaction effect if the lines diverge. According to the graph, the effect of interaction between feed and speed is greatest at high speeds, i.e., 2500 rpm, while it is minimal at middle and low speeds. The image also shows that low feed rates are where feed rate and spindle speed interact most. These numbers show that when drilling GFRP composites with a core drill, small feed rates with high spindle speeds are preferred.
Fig. 9. Interaction between the parameters on SN ratio of Grade Entropy Reasoning Grade
After finding the suitable optimal parameters, it is necessary to predict the grey fuzzy reasoning grade theoretically. The grey fuzzy reasoning grade can be predicted by using the following equation:

(14) 
where is the mean value of the gray fuzzy reasoning grade and is the gray fuzzy reasoning grade at the optimal level and m is the number of influential parameters that affect the multiple performance characteristics.
Table 10 shows the comparison results of the initial drilling parameters and the optimal drilling parameters. It is seen that thrust force at the initial setting level of s1f1 decreases from 143.5 to 61.5 (experiment number 21), a drastic decrease. Similarly, torque reduces from 0.48 to 0.2, delamination at the entry and exit decreases from 1.14 and 1.15 to 1.11 and 1.13, respectively. It is seen that the gray fuzzy reasoning grade is higher than that of the gray relational grade. From the above results, it has been asserted that fuzzy fuzzy reasoning can be useful for optimizing the multiple performances of CFRP composites in drilling.
Table 11 shows the response table for the gray fuzzy reasoning grade. In the gray fuzzy approach, to produce the best output, the optimal combination of the parameters as determined from the response table shows that spindle speed must be maintained at level 5 and feed rate at level 1. Feed rate has more influence on machining performance.
The percentage error in the current study is 9.38, compared to 14.78 in a study of a similar nature in the literature [55]. This shows that the proposed method can be effectively used for optimizing machining parameters during the drilling of composite laminates.
Table 10. Results of initial and optimal machining performance
Setting level 
Initial drilling parameters 
Optimal drilling parameters 

S1f1 
Prediction s5f1 
Experiment s5f1 

Pushout delamination 
1.15 
 
1.13 
Peelup delamination 
1.14 
 
1.11 
Thrust force 
143.5 
 
61.5 
Torque 
0.48 
 
0.2 
Grey relational grade 
0.548 
0.831 
0.939 
Grey fuzzy reasoning grade 
0.5 
0.828 
0.952 
Table 11. Response table of initial and optimal machining performance
Machining condition 
Level 1 
Level 2 
Level 3 
Level 4 
Level 5 
MaxMin 
Spindle speed, s 
0.414 
0.446 
0.485 
0.595 
0.610 
0.196 
Feed rate, f* 
0.733 
0.552 
0.454 
0.418 
0.393 
0.340* 
Overall mean grey entropy fuzzy grade=0.51 
The bold values indicate optimal levels, * more influencing parameter.
This study presents multiresponse optimization of the drilling of GFRP laminate by applying an innovative method combining the entropy method for weights, grey relational analysis, and fuzzy logic. Input factors are feed and speed, and the output responses are torque, thrust force, entry/peelup, and exit/pushout delamination factors. Depending on the results obtained, the below conclusions are drawn:
However, this study has the following limitations:
This research did not receive any specific grant from funding agencies in the public, commercial, or notforprofit sectors.
The author declares that there is no conflict of interest regarding the publication of this article.