International Journal of Polymer Science
Volume 2018 (2018), Article ID 8629894, 12 pages
https://doi.org/10.1155/2018/8629894

Research Article

Investigation of Drilling Parameters Using Grey Relational Analysis and Response Surface Methodology of Biaxial Glass Fibre Reinforced with Modified Epoxy Resin Composite

I Infanta Mary Priya¹ and B. K. Vinayagam²

¹Department of Mechanical Engineering, SRM Institute of Science and Technology, Chennai 603203, India
²Department of Mechatronics Engineering, SRM Institute of Science and Technology, Chennai 603203, India

Correspondence should be addressed to I Infanta Mary Priya; infanta.i@ktr.srmuniv.ac.in

Received 18 December 2017; Revised 14 May 2018; Accepted 19 May 2018; Published 27 June 2018

Academic Editor: Michele Zappalorto

Copyright © 2018 I Infanta Mary Priya and B. K. Vinayagam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

This research work attempts to study the most prominent factor of the drilling operations performed on different thicknesses of biaxial glass fibre reinforced with graphene platelet nanopowder and epoxy composite using three different drills. Damages are induced in the workpieces to analyse the effect of changed cutting parameters and different tool materials for varied thicknesses of the plates during the drilling process. The resultant drilled hole exhibited surface irregularities that are measured using SURFCOM 1400G. The circularity deviations of the holes are measured using a coordinate measuring machine. Image-processing technique is used to calculate the area of maximum diameter of the damaged zone. Using these data, delamination at entry and exit is calculated. Utilizing response surface methodology and grey relational analysis, the varied operations are carried out and analysed with different tool materials for common cutting parameters. It is found that the lesser thickness workpiece with selected HSS drill under high speed and low feed rate is the best variable option.

1. Introduction

Recent trends reveal that composite materials are extensively used in nearly all engineering fields from the automobile sector to the aircraft sector; these materials are favoured because of their inherent lightweight and achievable higher fibre aspect ratio. Rezende et al. [1] investigated the drill geometries on sandwich composites and observed that the tool selected and the speed were the most important factors which affected the thrust force, while the tool and feed rate played a major role in the burr height of the drilled hole. Though numerous research studies have been carried out in this area of machining process, very little literature documenting drilling operation data using different drill bits is available. Kumar et al. [2] studied the drilling process parameters such as feed, speed, and the drilled hole parameters such as delamination and surface roughness with three different materials of drill bits. For this study, the various drills used were HSS, carbide-tipped straight shank, and solid carbide eight-facet drill. The author concluded that the quality of the drilled holes was improved by using a solid carbide eight-facet drill. Babu et al. [3] studied the influence of drilling parameters on natural fibre-reinforced plastic with a cemented carbide drill, and the results were compared with GFRP composites. The analysis was carried out using the Taguchi technique as well as ANOVA. Thus, the authors were able to establish that feed rate and cutting velocity are the most influencing parameters with respect to delamination for various fibre-reinforced laminates. Various parts are manufactured using a FRP composite which requires machining operations such as drilling, milling, and grinding for the purpose of fastening, according to Grilo et al. [4]. Asiltürk and Neseli [5] developed a new method for the determination of optimal cutting parameters and a mathematical model for the evaluation of surface roughness. The system adopted for their study was noted to yield satisfactory results. Khashaba and El-Keran [6] studied the influence of speed and feed on thin glass fibre-reinforced woven composite. The parameters taken into consideration for the analysis were cutting temperature, thrust force, torque, delamination factor, surface roughness, and bearing strength. The results showed that the delamination factor, torque, and thrust force increased with an increase in feed while the temperature induced increased with a decrease in feed. Debnath et al. [7] developed an innovative drill which was designed and made for the purpose of drilling on composite laminates. The authors found that the occurrence of damages from the developed forces was reduced when the operation was performed using the newly developed drill bit tool. Kulkarni et al. [8] investigated the drilling parameters of glass fibre reinforced with a carbon black vinyl ester composite. It was concluded that delamination was minimum with a tungsten carbide tool. From the scanning electron microscopic images, it was inferred that the delamination at the entry was minimum when compared to that at the exit side of the hole. In their study, Mohan et al. [9] performed drilling operation on a glass fibre-reinforced polymer composite and conducted delamination analysis. Their study predicted that peel-up delamination is influenced by specimen thickness and cutting speed. Similarly, push-down delamination is influenced by specimen thickness and feed rate. Confirmation tests were conducted which yielded 99% confidence level with the predicted results. Mudhukrishnan et al. [10] studied the influence of tool materials on the surface roughness of the drilled hole of glass fibre-reinforced polypropylene composites. Their study noted the drilled hole had a better surface finish when a solid carbide drill was used. Palanikumar and Davim [11] investigated the influence of tool wear parameters while machining GFRP composites. The results obtained from the experimental work and the analysis determined that the cutting speed is the major factor that influences the tool wear, with feed rate parameter a close second. Palanikumar [12] developed a model to determine delamination and surface roughness using surface roughness methodology. His ANOVA analysis showed that the results were within 95% confidence level. Sardinas et al. [13] performed a multiobjective optimization study on the process of drilling parameters such as delamination and material removal rate. The optimization process was carried out using genetic algorithms. The obtained results were represented graphically to determine their suitability for various processes. Sridharan et al. [14] studied the drilling process parameters on nanophased jute fibre-reinforced polymer composite. The authors adopted image-processing technique for the determination of the delamination factor. They also concluded that the addition of nanofiller material such as graphene enhanced the machinability of the composite material. Vankanti and Ganta [15] optimized the drilling process parameters using the Taguchi method. The authors found that feed rate is the most promising factor which influences thrust force, and cutting speed is the major factor affecting the torque. This methodology helped them not only to reduce delamination but also to meet drilled hole standard tolerance levels.

From various available literatures, it is found that no research work has been reported so far on the performance of drilling operation on a biaxial GFRP graphene platelet nanopowder composite. Usually, the delamination at entry and exit is measured by machine vision technique. In this research work, two different methods are used for analysing the optimal drilling parameters. One method is response surface methodology and the other is grey relational analysis. It is found that by using these two methods, the optimal results obtained are the same. The most suitable tool for drilling a nano-based GFRP composite is the HSS drill bit, and it yields minimum delamination at the entry and exit of the drilled hole with the lesser thickness (2 mm) specimen under high speed and low feed rate operations. The hole drilled using the HSS tool also gives minimum surface roughness and maximum circularity when compared to other titanium-coated HSS and carbide tip drill tools.

2. Materials Used for the Study

This work involves the study of drilling operation on a biaxial glass fibre-reinforced polymer composite material. The material used for this study is a biaxial glass cloth of 600 gsm aerial density, purchased from Easy Composites, UK, and the laminates are prepared using hand lay-up method. Initially, bisphenol-A epoxy resin of grade LY556 is stirred thoroughly using a mechanical stirrer for 4 hrs, and then 0.1% weight of graphene platelet nanopowder is blended into the continuously stirred epoxy resin for another 4 hrs. Immediately after blending, 1 part of araldite hardener of grade HY951 is added to the blended resin mixture and infused to make the laminates. SEM image of the graphene platelet nanopowder is shown in Figure 1 to a magnification of 40,000x with particle size of 3 μm. Two sets of laminates are made to a thickness of 2 mm and 3 mm using the hand lay-up method. Then, the laminates are compressed in a compression moulding machine at 20 bar pressure and at a temperature of 80°C for 4 hrs after which it is allowed to cure for 24 hrs. Thus, the laminates are prepared and made ready for quality tests. They are then cut into test piece sizes of 100 × 100 mm. The drilling operation is performed in the vertical machining centre using three different drills (HSS drill, titanium-coated HSS, and carbide tip drill) of 10 mm diameter. The experimental set-up with the HSS drill bit is shown in Figure 2, and the various drills used are shown in Figure 3. Table 1 gives the specification details of the different material drills used for the present study.

Figure 1: SEM image of the graphene platelet nanopowder.

Figure 2: Experimental set-up.

Figure 3: Types of drill bits used for the drilling operation.

Table 1: Drilling details.

Parameter
Description

Drill tool materials
HSS drill, titanium-coated HSS drill, carbide tip drill

Diameter
10 mm

Geometry and type
Twist drill and straight shank

Point angle
118°

Machining condition
Dry

Feed rates (m/min)
50, 100, 150

Speed (rpm)
800, 1000, 1200

Figures 4(a) and 4(b) above show the drilled samples at the entry and exit sides, respectively, of the holes. Figure 4(a) shows that there is a minimum delamination at the entry side for all the three different drills while Figure 4(b) shows that there is maximum delamination with the titanium-coated HSS drill when compared to both the HSS drill and carbide tip drill at the exit side of the hole.

(a)

(b)

Figure 4: (a) Drilled samples at the entry side. (b) Drilled samples at the exit side.

3. Experimental Work

3.1. Delamination Measurement

Delamination during drilling operation occurs in two ways—peel up and push out. During drilling operation, the drill tool grazes the workpiece as the tool touches the specimen. The chips formed during the drilling operation gets pulled out in spiral form along the flute. As a consequence, the top surface of the laminate peels up first causing the defect called peel-up delamination. As the drilling operation progresses, the drill bit exerts compressive force which tends to bend the uncut plies elastically at the exit. At the same time, as the drill approaches the end of the process, there is a reduction in pressure due to less number of uncut plies which tends to reduce the resistance of bending in plies. Cracks develop adjacent to the hole because of increase in bending stress and weakening of interlaminar strength in the plies. As it drills down, the cracks get propagated further due to decrease in flexural rigidity. Due to this phenomenon, the bonding of interlamina fails which results in push-out delamination. But in the case of the carbide tip drill, there are two facets present for cutting, and there is a surface contact by means of the chisel edge of the tool. Since the concentration of the load at the surface contact increases, it causes irregularities around the drilled hole. The increased concentration of the load at the surface contact causes more irregularities in the area around the drilled hole.

Delamination is measured using machine vision Optiv Lite OLM 3020 model with a colour CCD camera of 1/3 high-resolution capacity attached with VMS 3.1 software. The set-up for measuring delamination is shown in Figure 5. The measured data are analysed using Minitab 17.

Figure 5: Delamination measurement at the entry and exit.

Delamination factor with the high-speed steel (HSS) drill at the entrance of the 2 mm sample is shown in Figure 6(a). It is less at low feed rate, and its value is 1.087, while the delamination factor at the entrance for the 3 mm thickness specimen is shown in Figure 6(b). It is less at higher feed rate, and it is 1.168 at 1200 rpm. Similarly, the delamination factor at the exit side of the 2 mm sample is minimum at 0.1 mm/min feed rate with a value of 1.023 while for the 3 mm sample, it is less at higher feed rate and its value is 1.131 at 1200 rpm, as shown in Figures 6(c) and 6(d). Therefore, the delamination of the 3 mm sample at the entry and exit is minimum under the same conditions while there is a small variation with respect to the 2 mm sample. However, comparing the 2 mm and 3 mm samples, both at the entry and exit sides, the delamination factor obtained with the 2 mm sample is the minimum. Also, the error bar is included to represent the variations in the measured parameter values.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

Figure 6: Delamination at entrance and exit under three different drills. (a, c, e, g, i, k) Delamination at the entry and exit of a 2 mm thickness specimen. (b, d, f, h, j, l) Delamination at the entry and exit of a 3 mm thickness specimen. (a, b) Delamination at the entrance. (c, d) Delamination at the exit. (e, f) Delamination at the entrance. (g, h) Delamination at the exit. (i, j) Delamination at the entrance. (k, l) Delamination at the exit.

The delamination factor with the titanium-coated HSS drill at the entrance of the 2 mm sample is shown in Figure 6(e). It is less at 0.1 mm/min feed rate and at 1200 rpm whose value is 1.028 while the delamination factor is minimum for the 3 mm sample at a feed rate of 0.1 mm/min and at 1000 rpm whose value is 1.031, as shown in Figure 6(f). Similarly, the delamination factor at the exit of the 2 mm sample is minimum at 0.1 mm/min feed rate and at 1200 rpm whose value is 1.037 while for the 3 mm sample, the delamination factor is minimum at 0.05 mm/min and at 1200 rpm whose value is 1.081. Therefore, delamination of the 2 mm sample at the entry and exit is minimum under the same conditions while there is a small variation with respect to the 3 mm sample. The delamination at the entry and exit is shown with an error bar in Figures 6(e)–6(h).

The delamination factor with the carbide tip drill at the entrance of the 2 mm sample is shown in Figure 6(i). It is minimum at 0.05 mm/min feed rate and at 1200 rpm whose value is 1.087 while the delamination factor is minimum for the 3 mm sample at 0.05 mm/min feed rate and at 1000 rpm whose value is 1.121, as shown in Figure 6(j). Similarly, the delamination factor at the exit of the 2 mm sample is minimum at 0.1 mm/min and at 1000 rpm whose value is 1.026 as shown in Figure 6(k) while the delamination factor for the 3 mm sample is minimum at 0.5 mm/min and at 1200 rpm whose value is 1.078, as shown in Figure 6(l). Therefore, it is inferred from the graphs that the delamination factor is minimum with the 2 mm sample when compared with the 3 mm sample. The error bar is also represented in the graphs to predict the uncertainty in the measured parameter values.

Hence, it is concluded from Figures 6(a)–6(l) that the usage of the HSS drill, titanium-coated HSS drill, and carbide tip drill yields less delamination factor both at the entry and exit with the 2 mm sample than the 3 mm sample.

3.2. Surface Roughness Measurement

Surface roughness is measured using a computerized surface roughness tester with a diamond stylus of 2 μm radius, and the set-up is shown in Figure 7.

Figure 7: Measurement of surface roughness.

The surface roughness of the hole drilled using the HSS drill and titanium-coated HSS drill is minimal at low feed rate and high speed. Similarly, the usage of a carbide tip drill tool follows a regular pattern with the 2 mm sample, and it is disturbed in the case of 1000 rpm. At 1000 rpm, there is a peak rise at maximum feed with the 2 mm sample. But as far as surface roughness is considered, it is minimal at maximum speed and at minimum feed rate with respect to the 2 mm sample. All the graphs from Figures 8(a)–8(c) are represented with an error bar.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 8: Surface roughness for 2 and 3 mm thickness specimens under three different drills. (a–c) Surface roughness of the 2 mm sample with (a) HSS drill, (b) titanium-coated HSS drill, and (c) carbide tip drill. (d–f) Surface roughness of the 3 mm sample with (d) HSS drill, (e) titanium-coated HSS drill, and (f) carbide tip drill.

Surface roughness is minimum at 0.1 mm/min feed rate and at high speed with respect to the 3 mm thick specimen of the HSS drilled hole. As the thickness of the workpiece is increased, the feed rate has to be increased further, as inferred from Figure 8(d). But when the titanium-coated HSS drill is considered, the surface roughness is minimum at high feed rate and high speed conditions as shown in Figure 8(e). The surface roughness is also minimum at maximum feed and speed when the hole is drilled with the carbide tip drill tool. In Figures 8(d)–8(f), the error bar is represented to show the variations in the measured values.

Thus, it is concluded that the surface roughness is minimum at less feed rate and high speed with the 2 mm sample while the surface roughness is minimum at high feed rate and high speed with the 3 mm sample. This is because as the selected thickness is increased, the feed rate needs to be increased further, so that the surface is smooth. According to Kumar et al., the occurrence of fracture is less under less feed and at high speed. The same criteria are also applicable to the current study. Apart from this, the present work deals with different thicknesses of the specimen. Kumar et al. observed that when the thickness was minimum, the conditions were satisfied but as the thickness of the specimen was increased, the above-stated conditions differed.

3.3. Circularity Measurement of Drilled Hole

Circularity is measured using a ZEISS Contura G2 coordinate measuring machine, and one of the profiles obtained is shown in Figure 9. Figure 9 represents the profile for the 3 mm thickness specimen drilled with the HSS drill tool material under 0.15 mm/min feed rate and 1000 rpm speed. The various control parameters and their levels are represented in Table 2.

Figure 9: Circularity measurement using CMM.

Table 2: Different control parameters and their levels.

Control parameter
Unit
Level 1
Level 2
Level 3

Thickness
mm
2
—
3

Drill bit
—
1
2
3

Feed
mm/min
0.05
0.1
0.15

Speed
rpm
800
1000
1200

4. Results and Discussion

4.1. Surface Roughness

ANOVA technique is used for determining the most significant statistical parameter which influences the drilling operation of a biaxial noncrimp fabric composite. It also determines the percentage contribution of each control parameter during the drilling process. The results of the ANOVA analysis are shown in Tables 3–6. Analysis is carried out to a confidence level of 95% (significance level is 5%). From Table 3, it is understood that the type of drill bit, speed, feed, and thickness influenced the surface roughness values by 55%, 4.73%, 1.12%, and 0.51%, respectively. Since the value is lower than 0.05, it is observed that the type of drill bit and speed have physical significance on surface roughness, especially the type of drill used for drilling purpose. Also, since the value is more than 0.05, it is considered as insignificant and it is ignored.

Table 3: ANOVA analysis for surface roughness.

Analysis of variance

Source
DF
Seq SS
Contribution
Adj SS
Adj MS
value
value

Model
13
247.686
95.33%
247.686
19.053
50.3
0

Linear
4
159.384
61.35%
163.418
40.855
107.86
0

Drill bit
1
142.891
55%
140.711
140.711
371.47
0

Feed
1
2.901
1.12%
4.785
4.785
12.63
0.001

Speed
1
12.277
4.73%
14.827
14.827
39.14
0

Square
3
30.065
11.57%
28.381
9.46
24.97
0

Drill bit  drill bit
1
22.863
8.80%
10.112
10.112
26.69
0

Feed  feed
1
6.474
2.49%
10.199
10.199
26.92
0

2-way interaction
6
58.237
22.42%
58.237
9.706
25.62
0

Thickness  drill bit
1
44.192
17.01%
50.761
50.761
134.01
0

Thickness  feed
1
10.067
3.87%
10.476
10.476
27.66
0

Drill bit  speed
1
2.308
0.89%
2.322
2.322
6.13
0.019

Error
32
12.121
4.67%
12.121
0.379

Total
45
259.808
100.00%

S
R-sq
R-sq (adj)
PRESS
R-sq (pred)

0.615460
95.33%
93.44%
24.3310
90.63%

Table 4: ANOVA analysis for circularity.

Source
DF
Seq SS
Contribution
Adj SS
Adj MS
value
value

Model
13
0.256581
79.58%
0.256581
0.019737
9.29
0

Linear
4
0.093656
29.05%
0.127721
0.03193
15.03
0

Thickness
1
0.010347
3.21%
0.012988
0.012988
6.11
0.019

Drill bit
1
0.018212
5.65%
0.034247
0.034247
16.12
0

Feed
1
0.045643
14.16%
0.07398
0.07398
34.83
0

Speed
1
0.019454
6.03%
0.020088
0.020088
9.46
0.004

Square
3
0.137807
42.74%
0.136883
0.045628
21.48
0

Drill bit  drill bit
1
0.039647
12.30%
0.058714
0.058714
27.64
0

Speed  speed
1
0.092445
28.67%
0.093571
0.093571
44.05
0

Thickness  feed
1
0.01357
4.21%
0.011942
0.011942
5.62
0.024

Error
31
0.065849
20.42%
0.065849
0.002124

Total
44
0.322431
100.00%

S
R-sq
R-sq (adj)
PRESS
R-sq (pred)

0.0460888
79.58%
71.01%
0.131806
59.12%

Table 5: ANOVA analysis for delamination entry.

Analysis of variance

Source
DF
Seq SS
Contribution
Adj SS
Adj MS
value
value

Model
13
0.03751
99.81%
0.03751
0.002885
530.76
0

Linear
4
0.021681
57.69%
0.007774
0.001944
357.52
0

Thickness
1
0.018327
48.77%
0.006198
0.006198
1140.17
0

Drill bit
1
0.000015
0.04%
0.000224
0.000224
41.22
0

Feed
1
0.003007
8.00%
0.000554
0.000554
101.93
0

Speed
1
0.000332
0.88%
0.000041
0.000041
7.61
0.016

Square
3
0.000468
1.25%
0.000359
0.00012
22.02
0

Drill bit  drill bit
1
0.000329
0.88%
0.000326
0.000326
59.93
0

Speed  speed
1
0
0.00%
0.000026
0.000026
4.78
0.048

2-way interaction
6
0.015362
40.88%
0.015362
0.00256
470.95
0

Thickness  drill bit
1
0.012946
34.45%
0.007243
0.007243
1332.37
0

Thickness  feed
1
0.000972
2.59%
0.00133
0.00133
244.62
0

Thickness  speed
1
0.000598
1.59%
0.000665
0.000665
122.39
0

Drill bit  feed
1
0.000773
2.06%
0.000477
0.000477
87.82
0

Feed  speed
1
0.00004
0.11%
0.00004
0.00004
7.36
0.018

Error
13
0.000071
0.19%
0.000071
0.000005

Total
26
0.037581
100.00%

S
R-sq
R-sq (adj)
PRESS
R-sq (pred)

0.0023316
99.81%
99.62%
0.0002890
99.23%

Table 6: ANOVA analysis for delamination exit.

Analysis of variance

Source
DF
Seq SS
Contribution
Adj SS
Adj MS
value
value

Model
13
0.058171
69.36%
0.058171
0.004475
5.05
0

Linear
4
0.023373
27.87%
0.024854
0.006214
7.01
0

Drill bit
1
0.00524
6.25%
0.004373
0.004373
4.94
0.034

Feed
1
0.012731
15.18%
0.016748
0.016748
18.9
0

Square
3
0.016344
19.49%
0.01552
0.005173
5.84
0.003

Feed  feed
1
0.015351
18.30%
0.012999
0.012999
14.67
0.001

2-way interaction
6
0.018454
22.01%
0.018454
0.003076
3.47
0.01

Thickness  feed
1
0.017181
20.49%
0.017772
0.017772
20.06
0

Error
29
0.025692
30.64%
0.025692
0.000886

Total
42
0.083863
100.00%

S
R-sq
R-sq (adj)
PRESS
R-sq (pred)

0.0297645
69.36%
55.63%
0.0577628
31.12%

4.2. Circularity

The most significant factor for circularity is feed rate with a contribution of 14.16% which is then followed by speed, drill bit material, and thickness of specimen. This inference is drawn on the basis of Table 4. Since the value is more than 0.05, it is considered as insignificant and it is ignored.

4.3. Delamination at Entry

The thickness, feed, speed, and drill bit affected the delamination entry by 48.77%, 8%, 0.88%, and 0.04%, respectively. The thickness of the specimen and feed rate had physical and statistical significance on delamination entry especially the thickness of the specimen. Table 5 gives this inference about the delamination entry of the drilled hole. Since the value is more than 0.05, it is considered as insignificant and it is ignored.

4.4. Delamination at Exit

For the delamination at exit, the most influencing factor is feed with 15.18% contribution which is then followed by drill bit, speed, and thickness. Table 6 represents these values at the exit side of the drilled hole. Since the value is more than 0.05, it is considered as insignificant and it is ignored.

The various residual plots for surface roughness, circularity, and delamination entry and exit are shown in Figures 10(a)–10(d). It is observed from the normal probability plots of all the four parameters that most of the values are best fitted with the straight line. The regression equations for surface roughness, circularity, and delamination entry and exit are developed using response surface methodology in order to predict the output responses. The generalized form of the regression equation is shown in the following:

where  is the constant of RSM; , , , and  are the coefficients of linear variables , , and , respectively; , , and  are the coefficients of squares of linear variables , , and , respectively; , , , , , and  are the coefficients of interaction of linear variables , , and , respectively.

where is the thickness, is the drill bit (i.e., 1-HSS, 2-Ti-coated HSS, and 3-carbide tip drill), is the feed, and is the speed.

(a)

(b)

(c)

(d)

Figure 10: Residual plots: (a) surface roughness, (b) circularity, (c) delamination at entry, and (d) delamination at exit.

Figure 11 represents the optimization plot for a drilling operation. It shows that the most optimal tool is the HSS drill bit, when the drilling process is carried out on a lesser thickness specimen under a feed rate of 0.08 mm/min and high speed (1200 rpm).

Figure 11: Optimization plot.

4.5. Grey Relational Analysis

Grey relational analysis is an effective measure of analysing the drilling parameter relationship. In this analysis, initial preprocessing of the data is done so as to transfer the original sequence into a comparable sequence. Due to this, the experimental results are normalized to a range of zero and one. After data preprocessing, the grey relational coefficient is expressed as a ratio of ideal and actual normalized results as depicted in the following equation with different parameters:

where is the deviation sequence of the reference sequence and the comparability sequence , namely,

is the identification coefficient and it is assumed to be equal to 0.5 usually, and the grey relational grade is given by the following equation:

For the present study, the target values are set as minimum for surface roughness and delamination at entry and exit and maximum for circularity. Also, from the experimental design, as observed from Figure 12 and Table 7, the drilling operation parameters set for experiment number 5 gives the best optimal performance characteristics among all the 54 experiments.

Figure 12: Grey relational grade versus experimental runs.

Table 7: Grey relational rank.

S. number
Circularity grey relational coefficient
Delamination entry grey relational coefficient
Delamination exit grey relational coefficient
Surface roughness grey relational coefficient
Grey relational grade
Rank

1
0.395296753
0.689373297
0.62529274
0.87487375
2.584836539
6

2
0.375931842
0.685636856
0.708222812
0.996031084
2.765822594
4

3
0.526080477
0.681940701
0.628235294
1
2.836256472
3

4
0.339097022
0.664041995
0.439868204
0.89231715
2.335324371
16

5
0.535660091
0.65374677
1
0.959617618
3.149024479
1

6
0.397075366
0.643765903
0.397913562
0.96409658
2.402851411
13

7
0.363542739
0.630922693
0.388646288
0.690251269
2.07336299
31

8
0.456662354
0.624691358
0.970909091
0.686720798
2.738983601
5

9
0.457846952
0.618581907
0.530815109
0.78087968
2.388123649
14

10
0.554160126
0.612590799
0.631205674
0.471489399
2.269445997
18

11
0.433128834
0.469387755
0.53722334
0.542447351
1.982187281
35

12
0.340405014
0.587006961
0.875409836
0.683817818
2.486639629
9

13
0.718940937
0.410048622
0.518446602
0.461875194
2.109311355
28

14
0.507913669
0.342354533
0.333333333
0.471903695
1.65550523
53

15
0.552425665
1
0.905084746
0.548317934
3.005828344
2

16
0.333333333
0.537154989
0.514450867
0.415757041
1.800696231
48

17
0.375931842
0.44
0.482820976
0.421860885
1.720613704
52

18
0.535660091
0.412724307
0.441322314
0.428560029
1.818266741
43

19
0.461437908
0.647058824
0.643373494
0.416269426
2.168139652
26

20
0.398870056
0.515274949
0.74789916
0.380522195
2.04256636
31

21
0.733887734
0.681940701
0.407633588
0.442435227
2.265897249
19

22
0.466314399
0.553610503
0.445742905
0.414694413
1.88036222
40

23
0.411901984
0.515274949
0.978021978
0.443384933
2.348583844
15

24
0.579638752
0.667546174
0.610983982
0.443055727
2.301224635
17

25
0.439601494
0.452593918
0.345407503
0.383292296
1.620895211
54

26
0.409988386
0.47645951
0.73553719
0.333333333
1.955318419
37

27
0.435265105
0.472897196
0.461139896
0.442982637
1.812284834
46

28
0.339097022
0.426644182
0.435562806
0.535470362
1.736774373
51

29
0.420738975
0.407407407
0.462738302
0.526876024
1.817760708
44

30
0.710261569
0.444639719
0.493530499
0.615050734
2.263482521
20

31
0.362051282
0.428087986
0.438423645
0.661350902
1.889913816
38

32
0.340405014
0.433962264
0.459552496
0.609556779
1.843476553
42

33
0.804100228
0.464220183
0.44278607
0.700149925
2.411256406
12

34
0.410942957
0.450980392
0.539393939
0.588283621
1.989600909
33

35
1
0.444639719
0.481081081
0.5800553
2.5057761
8

36
0.436341162
0.47467167
0.552795031
0.670432557
2.13424042
27

37
0.972451791
0.452593918
0.569296375
0.481741283
2.476083367
10

38
0.521418021
0.576309795
0.675949367
0.487717386
2.261394569
22

39
0.433128834
0.333333333
0.697127937
0.525304198
1.988894303
34

40
0.716024341
0.546436285
0.530815109
0.409018903
2.202294638
24

41
0.461437908
0.976833977
0.448739496
0.375938008
2.262949389
21

42
0.7827051
0.44
0.416536661
0.387915779
2.02715754
32

43
0.470039947
0.465930018
0.469244288
0.481650553
1.886864807
39

44
0.433128834
0.469387755
0.419152276
0.46251561
1.784184475
49

45
0.436341162
0.367198839
0.516441006
0.536417028
1.856398035
41

46
0.834515366
0.551198257
0.602708804
0.428696867
2.417119294
11

47
0.502133713
0.576309795
0.579175705
0.445666155
2.103285368
29

48
0.718940937
0.455855856
0.518446602
0.539228483
2.232471878
23

49
0.468791501
0.429541596
0.445742905
0.462312553
1.806388554
47

50
0.333333333
0.433962264
0.469244288
0.535999441
1.772539327
50

51
0.461437908
0.568539326
0.481081081
0.689985225
2.201043541
25

52
0.420738975
0.459165154
0.524557957
0.412972433
1.817434519
45

53
0.375931842
0.423785595
0.669172932
0.493630281
1.96252065
36

54
0.526080477
0.551198257
0.708222812
0.789315109
2.574816654
7

5. Conclusion

From the present study, the following points are concluded:

(i)Using response surface methodology, the most optimal drilling parameters for drilling biaxial GFRP with a graphene platelet nanopowder composite are found to be with the HSS drill bit on 2 mm thickness specimen under limiting factors of high speed and low feed rate.(ii)Using grey relational analysis, the most optimal conditions for drilling biaxial GFRP with a graphene platelet nanopowder composite is found to be with the HSS drill on 2 mm thickness specimen with low feed rate at the selected 1000 rpm speed.

Therefore, by comparing the two methods, the most optimal conditions of the drilling process are found to be the same. Thus, for minimum thickness of biaxial GFRP with the graphene platelet nanopowder composite, the HSS drill suits well and the delamination at the entry and exit is minimum with the 2 and 3 mm thickness specimens. Also, the surface roughness is minimum, and the circularity is maximum with the 2 mm thickness specimen which is drilled with the HSS drill bit.

Hence, it is concluded that for the biaxial nanocomposite, the drilling operation performed using the HSS drill bit on 2 mm thickness specimen under high speed and low feed rate yielded minimum delamination at the entry and exit, minimum surface roughness, and maximum circularity when compared to titanium-coated HSS drill and carbide tip drill tools.

Conflicts of Interest

The authors declare that there is no conflict of interest regarding the publication of this paper.

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