1 Introduction
2 Materials and methods
3 Composite fabrication
4 Machining parameters
Unit | Notation | Level 1 | Level 2 | Level 3 | Level 4 | |
---|---|---|---|---|---|---|
Filler % | wt% | Filler % | 0 | 2 | 4 | 6 |
Water pressure | MPa | WP | 200 | 230 | 260 | 290 |
Transverse speed | mm/min | TS | 30 | 40 | 50 | 60 |
Stand-off distance | mm | SOD | 1 | 2 | 3 | 4 |
Exp. no | Filler % | WP | TS | SOD | MRR | Ra | Kt | SN ratio for MRR | SN ratio for Ra | SN ratio for Kt |
---|---|---|---|---|---|---|---|---|---|---|
1 | 0 | 200 | 30 | 1 | 2.03 | 3.57 | 0.5336 | 6.1499 | − 11.0534 | 5.45568 |
2 | 0 | 230 | 40 | 2 | 4.05 | 3.59 | 0.5667 | 12.1491 | − 11.1019 | 4.93294 |
3 | 0 | 260 | 50 | 3 | 6.07 | 3.87 | 0.6959 | 15.6638 | − 11.7542 | 3.14906 |
4 | 0 | 290 | 60 | 4 | 6.75 | 3.99 | 0.7409 | 16.5861 | − 12.0195 | 2.60481 |
5 | 2 | 200 | 40 | 3 | 3.72 | 3.71 | 0.6144 | 11.4109 | − 11.3875 | 4.23098 |
6 | 2 | 230 | 30 | 4 | 2.25 | 3.55 | 0.6016 | 7.0437 | − 11.0046 | 4.41384 |
7 | 2 | 260 | 60 | 1 | 5.51 | 3.66 | 0.5519 | 14.8230 | − 11.2696 | 5.16279 |
8 | 2 | 290 | 50 | 2 | 5.64 | 3.63 | 0.5061 | 15.0256 | − 11.1981 | 5.91527 |
9 | 4 | 200 | 50 | 4 | 4.53 | 3.84 | 0.7244 | 13.1220 | − 11.6866 | 2.80043 |
10 | 4 | 230 | 60 | 3 | 5.31 | 3.86 | 0.6616 | 14.5019 | − 11.7317 | 3.58809 |
11 | 4 | 260 | 30 | 2 | 2.01 | 3.3 | 0.3919 | 6.0639 | − 10.3703 | 8.13649 |
12 | 4 | 290 | 40 | 1 | 3.27 | 3.24 | 0.4061 | 10.2910 | − 10.2109 | 7.82734 |
13 | 6 | 200 | 60 | 2 | 4.16 | 3.89 | 0.6016 | 12.3819 | − 11.7990 | 4.41384 |
14 | 6 | 230 | 50 | 1 | 3.65 | 3.57 | 0.4399 | 11.2459 | − 11.0534 | 7.13292 |
15 | 6 | 260 | 40 | 4 | 3.44 | 3.52 | 0.5072 | 10.7312 | − 10.9309 | 5.89642 |
16 | 6 | 290 | 30 | 3 | 2.72 | 3.23 | 0.3492 | 8.6914 | − 10.1841 | 9.13852 |
5 Results and discussion
5.1 Effect of machining parameters on material removal rate
Levels | Filler % | WP | TS | SOD |
---|---|---|---|---|
1 | 12.637 | 10.766 | 6.987 | 10.627 |
2 | 12.076 | 11.235 | 11.146 | 11.405 |
3 | 10.995 | 11.82 | 13.764 | 12.567 |
4 | 10.763 | 12.648 | 14.573 | 11.871 |
Delta | 1.875 | 1.882 | 7.586 | 1.94 |
Rank | 4 | 3 | 1 | 2 |
Source | df | Seq SS | Adj SS | Adj MS | F | P | Contribution (%) |
---|---|---|---|---|---|---|---|
Filler % | 3 | 3.5629 | 3.5629 | 1.1876 | 23.6 | 0.014 | 11.01 |
WP | 3 | 2.3496 | 2.3496 | 0.7832 | 15.56 | 0.025 | 7.26 |
TS | 3 | 24.7069 | 24.7069 | 8.2356 | 163.66 | 0.001 | 76.36 |
SOD | 3 | 1.5841 | 1.5841 | 0.528 | 10.49 | 0.042 | 4.90 |
Error | 3 | 0.151 | 0.151 | 0.0503 | |||
Total | 15 | 32.3545 |
5.2 Effect of machining parameters on surface roughness
Level | Filler % | WP | TS | SOD |
---|---|---|---|---|
1 | − 11.48 | − 11.48 | − 10.65 | − 10.9 |
2 | − 11.21 | − 11.22 | − 10.91 | − 11.12 |
3 | − 11 | − 11.08 | − 11.42 | − 11.26 |
4 | − 10.99 | − 10.9 | − 11.7 | − 11.41 |
Delta | 0.49 | 0.58 | 1.05 | 0.51 |
Rank | 4 | 2 | 1 | 3 |
Source | df | Seq SS | Adj SS | Adj MS | F | P | Contribution (%) |
---|---|---|---|---|---|---|---|
Filler % | 3 | 0.106125 | 0.106125 | 0.035375 | 9.21 | 0.049 | 13.15 |
WP | 3 | 0.113875 | 0.113875 | 0.037958 | 9.88 | 0.046 | 14.11 |
TS | 3 | 0.473525 | 0.473525 | 0.157842 | 41.09 | 0.006 | 58.66 |
SOD | 3 | 0.102125 | 0.102125 | 0.034042 | 8.86 | 0.053 | 12.65 |
Error | 3 | 0.011525 | 0.011525 | 0.003842 | |||
Total | 15 | 0.807175 |
5.3 Effect of machining parameters on kerf taper
Level | Filler % | WP | TS | SOD |
---|---|---|---|---|
1 | 4.036 | 4.225 | 6.786 | 6.395 |
2 | 4.931 | 5.017 | 5.722 | 5.85 |
3 | 5.588 | 5.586 | 4.749 | 5.027 |
4 | 6.645 | 6.371 | 3.942 | 3.929 |
Delta | 2.61 | 2.146 | 2.844 | 2.466 |
Rank | 2 | 4 | 1 | 3 |
Source | df | Seq SS | Adj SS | Adj MS | F | P | Contribution (%) |
---|---|---|---|---|---|---|---|
Filler % | 3 | 0.052118 | 0.052118 | 0.017373 | 22.65 | 0.015 | 24.59 |
WP | 3 | 0.029923 | 0.029923 | 0.009974 | 13 | 0.032 | 14.12 |
TS | 3 | 0.067041 | 0.067041 | 0.022347 | 29.13 | 0.01 | 31.63 |
SOD | 3 | 0.060605 | 0.060605 | 0.020202 | 26.34 | 0.012 | 28.59 |
Error | 3 | 0.002301 | 0.002301 | 0.000767 | |||
Total | 15 | 0.211987 |
5.4 Multi-objective optimization by CRITIC-coupled COPRAS approach
5.4.1 Development of CRITIC modelling
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Step 1: Construction of decision matrix based on output values shown in Eq. (1)$$D={\left[{D}_{ij}\right]}_{n\times m}=\left[\begin{array}{c}{{\text{D}}}_{11} {{\text{D}}}_{12}\dots .{{\text{D}}}_{1m}\\ {{\text{D}}}_{21} {{\text{D}}}_{22}\dots .{{\text{D}}}_{2m}\\ . . .\\ {{\text{D}}}_{n1} {{\text{D}}}_{n2}\dots .{{\text{D}}}_{nm}\end{array}\right]$$(1)
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Step 2: Normalization of attained decision matrix using Eq. (2)where min(Dij) denotes the minimal function and max(Dij) represents the maximum function. The normalized values are showcased in Table9. Herein, for MRR, the higher value is selected as maximum function, while lower values are selected as maximum function for surface roughness and kerf angle.Table 9Normalized decision matrix obtained in the CRITIC methodRunNormalization MRRNormalization RaNormalization Kt10.00420.55260.529220.43040.52630.444730.85650.15790.114941.00000.00000.000050.36080.36840.323060.05060.57890.355670.73840.43420.482580.76580.47370.599490.53160.19740.0421100.69620.17110.2025110.00000.90790.8910120.26580.98680.8547130.45360.13160.3556140.34600.55260.7684150.30170.61840.5966160.14981.00001.0000$${D}_{ij}^{+}=\frac{{D}_{ij}-{\text{min}}({D}_{ij})}{{\text{max}}\left({D}_{ij}\right)-{\text{min}}({D}_{ij})}$$(2)
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Step 3: Formulating the correlation coefficient by Eq. (3)where \({\sigma }_{j}\) represents the standard deviation of jth response and rij represents the correlation coefficient among the output factors.$${{\text{Co}}}_{j}={\sigma }_{j}\times \sum \nolimits_{j=1}^{n}(1-{r}_{ij})$$(3)
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Step 4: Weight determination for each output response by using Eq. (4)$${{\text{IW}}}_{j}=\frac{{{\text{Co}}}_{j}}{\sum_{j=1}^{n}{{\text{Co}}}_{j}}$$(4)
MRR | Ra | Kt | Coj | IWj | |
---|---|---|---|---|---|
MRR | 1 | − 0.7358 | − 0.6347 | 1.0443 | 0.4930 |
Ra | − 0.7358 | 1 | 0.9214 | 0.5538 | 0.2615 |
Kt | − 0.6347 | 0.9214 | 1 | 0.5200 | 0.2455 |
5.4.2 CRITIC-coupled COPRAS approach
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Step 1: The initial step the choice matrix is created, then the output parameter is normalized by$${{\text{NO}}}_{ij}=\frac{{Q}_{ij}}{\sqrt{\sum_{i=1}^{m}{{Q}_{ij}}^{2}}}$$(5)
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Step 2: Calculated individual weight is multiplied to a normalized decision matrix in this process as shown in Eq. (6). Here, the normalized matrix (Eq. (5)) will be multiplied by the weightage computed from the CRITIC approach (Eq. (4)) to create the weighted matrix displayed in Table 11 where NWij is the weighted normalized value.$${{\text{NW}}}_{ij}={{\text{IW}}}_{j} \times {{\text{NO}}}_{ij}$$(6)Table 11Computed attribute valuesNormalized matrixWeighted normalized matrixPiRiMRRRaKtMRRRaKtMRRRa0.031100.061500.060000.021720.001380.016850.021720.018770.062200.061800.063720.043340.001390.017890.043340.019820.093200.066700.078250.064960.001490.021970.064960.024050.103600.068700.083310.072240.001540.023400.072240.025540.057100.063900.069090.039810.001430.019400.039810.021390.034500.061100.067650.024080.001370.019000.024080.020900.084600.063000.062060.058970.001410.017430.058970.019390.086600.062500.056910.060360.001400.015980.060360.017930.069500.066100.081460.048480.001480.022870.048480.024940.081500.066500.074400.056830.001490.020890.056830.022960.030800.056800.044070.021510.001270.012380.021510.014150.050200.055800.045670.034990.001250.012820.034990.014560.063800.067000.067650.044520.001500.019000.044520.021090.056000.061500.049470.039060.001380.013890.039060.015810.052800.060600.057030.036810.001360.016020.036810.017910.041700.055600.039270.029110.001250.011030.029110.01276
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Step 3: Pi calculationwhere Pi denotes the maximization of function calculated using Eq. (7) and n is the number of maximum response. In this research, MRR is considered as the maximization since higher MRR improves the machining performance.$${P}_{i}=\sum \nolimits_{j=1}^{n}{Q}_{ij}$$(7)
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Step 4: Calculation of Riwhere Ri implies the minimization of the function calculated based on Eq. (8). Herein, Ra and Kt are considered as the minimization function since lower Ra and Kt deliver better surface quality.$${R}_{i}=\sum \nolimits_{j=m+1}^{n}{Q}_{ij}$$(8)
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Step 5: Perceiving the diminutive value of R$${R}_{{\text{min}}}={\text{min}} {R}_{i}$$(9)
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Step 6: Weight determination on individual response Qi
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Step 7: Utility degree Ni % determination$${N}_{i}=100\times ({Q}_{i}/{Q}_{{\text{max}}})$$(11)
Rmin/Ri | Qi | Ni (%) | Ranking |
---|---|---|---|
0.67995 | 0.02226 | 30.50782 | 15 |
0.64373 | 0.04391 | 60.17605 | 8 |
0.53051 | 0.06565 | 89.96846 | 2 |
0.49966 | 0.07297 | 100.00000 | 1 |
0.59646 | 0.04042 | 55.39746 | 9 |
0.61045 | 0.02468 | 33.81810 | 14 |
0.65799 | 0.05952 | 81.57275 | 4 |
0.71166 | 0.06087 | 83.42221 | 3 |
0.51171 | 0.04919 | 67.41619 | 6 |
0.55566 | 0.05748 | 78.77912 | 5 |
0.90197 | 0.02191 | 30.03374 | 16 |
0.87620 | 0.03541 | 48.53018 | 12 |
0.60516 | 0.04512 | 61.83881 | 7 |
0.80722 | 0.03951 | 54.15225 | 10 |
0.71262 | 0.03732 | 51.15432 | 11 |
0.99994 | 0.02947 | 40.39294 | 13 |
5.5 Surface morphology of machined surface
6 Conclusions
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Among all the input parameters, BN addition mainly affects the kerf taper, while stand-off distance and water pressure mainly affect the material removal rate and surface roughness. Increasing the addition of BN reduces the kerf taper and improves the surface finishing, although it also slightly reduces the material removal rate.
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ANOVA results depict that transverse speed is the most influencing parameter over all the considered responses with the highest average contribution of 55.55%, while water pressure has the lowest average contribution of 11.83%. Contour plot analysis reveals that combination of higher water pressure with minimal filler percentage delivers better MRR; however, the same condition showcases higher values of surface roughness and kerf taper angle.
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CRITIC-COPRAS approach is able to identify the optimal cutting parameters (290 MPa water pressure, 60 mm/min transverse speed and 4 mm stand-off distance) for better production rate and high machined surface quality, leading to 6.20 mm3/min of MRR with 0.29° kerf taper angle and 3.86 µm minimal surface roughness.
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Formation of larger cracks and craters are identified on the machined surface through SEM analysis for the composite without filler addition, whereas a smooth machined surface is visualized for filler-added composites.
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In the future, machine learning approaches such as artificial neural network (ANN) and support vector machine (SVM) can be utilized to predict the MRR, Ra, and Kt for the developed novel composite by training the neural network with more experimental data.