Optimization and Modeling of Process Parameters in Multi-Hole Simultaneous Drilling Using Taguchi Method and Fuzzy Logic Approach
Abstract
:1. Introduction
2. Materials and Methods
3. Results and Discussion
3.1. Regression Analysis
3.2. Optimization of Drilling Conditions Using Taguchi Analysis
3.3. Prediction of Surface Roughness and Hole Size at Optimal Levels
3.4. Analysis of Variance
3.5. Fuzzy Modeling for Surface Roughness and Hole Size
3.6. Validations of Results
4. Conclusions
- Cutting speed and feed rate in the drilling of Al5083 have a significant impact on both types of drilling process i.e., one-shot drilling and multi-hole drilling. A higher cutting speed generates more heat, which increases the temperature at the hole boundaries, where the chips can easily be clogged over the flutes of the drills. Furthermore, it is speculated that more vibration is likely to be present due to the rotary motion of the tool. In addition, the size of the chips increases with an increase in the feed rate. Therefore, a higher cutting speed and feed rate can affect both the surface roughness and hole size.
- The ANOVA results revealed that for both drilling types, the cutting speed and feed rate are influential on the surface roughness and hole size, respectively. The percent influence of cutting speed on the surface roughness is 40.16%, whereas the feed rate has a 25.02% contribution. In the case of hole size, the deviation from the nominal drill size is more affected by the feed rate, which has a 61.31% contribution, and the significance of the cutting speed is 28.72%.
- The Taguchi method was shown to successfully analyze the optimal combination of process parameters for surface roughness and hole size, as achieved in multi-hole drilling with a lower cutting speed and feed rate. Therefore, in comparison to one-shot drilling, a poly-drill head can produce better hole quality and is capable of forming multi-holes simultaneously, which would help in acquiring good productivity even at the lower levels of drilling parameters.
- The fuzzy modeling successfully investigated the surface roughness and hole size in multi-hole drilling. The predicted data is closely correlated to the experimental results with a very small percentage error. Thus, the developed fuzzy model is reliable for the prediction of hole quality at different levels of process parameters, where notable savings in time and cost could be obtained.
- In regression analysis, the values of R2 are more than 80%, which shows that the responses with respect to the machining variables could be easily predicted. The validation experiment reveals that the developed model can be used for predicting better hole quality using a poly-drill head for multi-hole drilling. The average error between each comparison was found to be small and hence, the optimization by the Taguchi method and prediction of values for surface roughness and hole size using fuzzy logic are both acceptable.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Process | Material | Considered Process Parameters | Objectives | Optimization/Prediction Technique | Ref |
---|---|---|---|---|---|
OSD | AISI 4140 steel | DG, CS, and FR | CYL, PER, CON | Taguchi, ANOVA | [16] |
OSD | CFRP | SS, FR, and D | TF, T, DL | ANOVA analysis, Fuzzy logic | [17] |
OSD | Hybrid polymer composites | SS, FR, and D | TF, T, DL | Gray relational analysis, regression, fuzzy logic, and artificial neural network models | [10] |
Milling | hardened Steel (steel 1.2738) | CS, FR, radial depth, and axial depth | SR | Taguchi optimization technique, ANOVA, | [9] |
OSD | Al6063/Al2O3/Gr hybrid composite | SS, FR, and wt % of alumina | SR | Taguchi method | [18] |
OSD | CFRP | SS, FR, and D | TF, T, DL | Taguchi method, Principal component analysis, Fuzzy inference system | [19] |
OSD | GFRP | SS, FR, point angle, and chisel edge width | TF, T, SR, C | Taguchi, ANOVA | [8] |
OSD | Al 7075 | Tool, FR, and CS | TEMP | Taguchi method, ANOVA | [20] |
End milling | GRFP | SS, FR, and d | TL | Fuzzy logic | [21] |
Turning | CFRP | CS, feed, and d | SR | Fuzzy rule-based modeling | [22] |
OSD | Al-7075 | CS, FR, and point angle, | H, SR | Taguchi method and response surface methodology | [23] |
OSD | GFRP | SS, FR, and D | SR | Fuzzy logic and ANOVA | [11] |
OSD | Al 2024 | Drilling depth, FR, CS, and drilling tool | Diametral error, SR | Regression model, Taguchi optimization method, ANOVA | [2] |
Levels | Process Parameters | ||
---|---|---|---|
Drilling Type | Cutting Speed | Feed Rate | |
1 | One-shot drilling | 19 | 0.04 |
2 | Multi-spindle drilling | 38 | 0.08 |
3 | – | 57 | 0.14 |
Experiment No. | Control Factors | ||
---|---|---|---|
Drilling Type | Cutting Speed | Feed Rate | |
1 | One-shot drilling | 19 | 0.04 |
2 | 19 | 0.08 | |
3 | 19 | 0.14 | |
4 | 38 | 0.04 | |
5 | 38 | 0.08 | |
6 | 38 | 0.14 | |
7 | 57 | 0.04 | |
8 | 57 | 0.08 | |
9 | 57 | 0.14 | |
10 | Multi-spindle drilling | 19 | 0.04 |
11 | 19 | 0.08 | |
12 | 19 | 0.14 | |
13 | 38 | 0.04 | |
14 | 38 | 0.08 | |
15 | 38 | 0.14 | |
16 | 57 | 0.04 | |
17 | 57 | 0.08 | |
18 | 57 | 0.14 |
Trial No. | Orthogonal Array with Control Factors | Experimental Results | S/N Ratio | ||||
---|---|---|---|---|---|---|---|
Drilling Type | Cutting Speed | Feed Rate | Surface Roughness | Hole Size | Surface Roughness | Hole Size | |
1 | 1 | 1 | 1 | 3.561 | 6.040 | −11.030 | −15.620 |
2 | 1 | 1 | 2 | 4.209 | 6.048 | −12.483 | −15.632 |
3 | 1 | 1 | 3 | 4.657 | 6.056 | −13.362 | −15.644 |
4 | 1 | 2 | 1 | 4.422 | 6.043 | −12.912 | −15.625 |
5 | 1 | 2 | 2 | 4.522 | 6.052 | −13.107 | −15.638 |
6 | 1 | 2 | 3 | 4.699 | 6.062 | −13.441 | −15.652 |
7 | 1 | 3 | 1 | 4.808 | 6.047 | −13.639 | −15.631 |
8 | 1 | 3 | 2 | 5.022 | 6.059 | −14.017 | −15.648 |
9 | 1 | 3 | 3 | 6.933 | 6.073 | −16.818 | −15.669 |
10 | 2 | 1 | 1 | 3.457 | 6.036 | −10.775 | −15.615 |
11 | 2 | 1 | 2 | 3.718 | 6.044 | −11.405 | −15.627 |
12 | 2 | 1 | 3 | 4.344 | 6.054 | −12.757 | −15.641 |
13 | 2 | 2 | 1 | 3.676 | 6.039 | −11.307 | −15.620 |
14 | 2 | 2 | 2 | 4.126 | 6.049 | −12.311 | −15.633 |
15 | 2 | 2 | 3 | 4.626 | 6.059 | −13.304 | −15.648 |
16 | 2 | 3 | 1 | 4.566 | 6.048 | −13.191 | −15.632 |
17 | 2 | 3 | 2 | 4.990 | 6.061 | −13.961 | −15.651 |
18 | 2 | 3 | 3 | 5.724 | 6.075 | −15.154 | −15.671 |
Level | Surface Roughness | |||||
---|---|---|---|---|---|---|
Average Response Values | S/N Ratio Response Values | |||||
Drilling Type | Cutting Speed | Feed Rate | Drilling Type | Cutting Speed | Feed Rate | |
1 | 4.759 | 3.991 a | 4.082 a | −13.423 | −11.969 a | −12.142 a |
2 | 4.358 a | 4.345 | 4.431 | −12.685 a | −12.730 | −12.881 |
3 | – | 5.340 | 5.164 | – | −14.463 | −14.139 |
Level | Hole size | |||||
---|---|---|---|---|---|---|
Average Response Values | S/N Ratio Response Values | |||||
Drilling Type | Cutting Speed | Feed Rate | Drilling Type | Cutting Speed | Feed Rate | |
1 | 6.053 | 6.046 a | 6.042 a | −15.640 | −15.630 a | −15.624 a |
2 | 6.052 a | 6.051 | 6.052 | −15.637 a | −15.636 | −15.638 |
3 | – | 6.060 | 6.063 | – | −15.650 | −15.654 |
Source | Degrees of Freedom | Sequential Sum of Squares | Contribution | Adjusted Sum of Squares | Adjusted Mean Square | F-Value | P-Value |
---|---|---|---|---|---|---|---|
Model | 19 | 36.0261 | 82.08% | 36.0261 | 1.89611 | 8.2 | 0 |
CS | 2 | 17.6251 | 40.16% | 17.6251 | 8.81254 | 38.09 | 0 |
FR | 2 | 10.9826 | 25.02% | 10.9826 | 5.49129 | 23.74 | 0 |
DT | 1 | 2.1673 | 4.94% | 2.1673 | 2.16731 | 9.37 | 0.004 |
2-Way Interactions | 8 | 2.4065 | 5.48% | 2.4065 | 0.30081 | 1.3 | 0.276 |
CS x FR | 4 | 2.2008 | 5.01% | 2.2008 | 0.55019 | 2.38 | 0.071 |
CS x DT | 2 | 0.0825 | 0.19% | 0.0825 | 0.04126 | 0.18 | 0.837 |
FR x DT | 2 | 0.1232 | 0.28% | 0.1232 | 0.06159 | 0.27 | 0.768 |
3-Way Interactions | 4 | 1.5096 | 3.44% | 1.5096 | 0.3774 | 1.63 | 0.189 |
CS x FR x DT | 4 | 1.5096 | 3.44% | 1.5096 | 0.3774 | 1.63 | 0.189 |
Error | 34 | 7.8658 | 17.92% | 7.8658 | 0.23135 | – | – |
Total | 53 | 43.8919 | 100.00% | – | – | – | – |
Source | Degrees of Freedom | Sequential Sum of Squares | Contribution | Adjusted Sum of Squares | Adjusted Mean Square | F-Value | P-Value |
---|---|---|---|---|---|---|---|
Model | 19 | 0.00622 | 94.34% | 0.00622 | 0.000327 | 29.84 | 0 |
CS | 2 | 0.001893 | 28.72% | 0.001893 | 0.000947 | 86.31 | 0 |
FR | 2 | 0.004042 | 61.31% | 0.004042 | 0.002021 | 184.24 | 0 |
DT | 1 | 0.000037 | 0.57% | 0.000037 | 0.000037 | 3.42 | 0.073 |
2-Way Interactions | 8 | 0.000211 | 3.21% | 0.000211 | 0.000026 | 2.41 | 0.035 |
CS × FR | 4 | 0.000148 | 2.24% | 0.000148 | 0.000037 | 3.37 | 0.02 |
CS × DT | 2 | 0.000061 | 0.93% | 0.000061 | 0.00003 | 2.78 | 0.076 |
FR × DT | 2 | 0.000002 | 0.04% | 0.000002 | 0.000001 | 0.11 | 0.896 |
3-Way Interactions | 4 | 0.000003 | 0.04% | 0.000003 | 0.000001 | 0.06 | 0.992 |
CS × FR × DT | 4 | 0.000003 | 0.04% | 0.000003 | 0.000001 | 0.06 | 0.992 |
Error | 34 | 0.000373 | 5.66% | 0.000373 | 0.000011 | – | – |
Total | 53 | 0.006593 | 100% | – | - | – | – |
Membership Function Type | Variable | Fuzzy Input | Fuzzy Output | ||||||
---|---|---|---|---|---|---|---|---|---|
Cutting Speed | Feed Rate | Surface Roughness | Hole Size | ||||||
Parameter | Range | Parameter | Range | Parameter | Range | Parameter | Range | ||
Triangular | VVL | (12 15 18) | (12 66) | (0.01 0.02 0.03) | (0.01 0.19) | (3 3.15 3.3) | (3 6.8) | (6.01 6.015 6.02) | (6.01 6.1) |
VL | (18 21 24) | (12 66) | (0.03 0.04 0.05) | (0.01 0.19) | (3.3 3.55 3.7) | (3 6.8) | (6.02 6.025 6.03) | (6.01 6.1) | |
L | (24 27 30) | (12 66) | (0.05 0.06 0.07) | (0.01 0.19) | (3.559 3.783 4.005) | (3 6.8) | (6.03 6.035 6.04) | (6.01 6.1) | |
ML | (30 33 36] | (12 66) | (0.07 0.08 0.09) | (0.01 0.19) | (3.783 3.95 4.117) | (3 6.8) | (6.04 6.045 6.05) | (6.01 6.1) | |
M | (36 39 42) | (12 66) | (0.09 0.1 0.11) | (0.01 0.19] | (4.117 4.35 4.5) | (3 6.8] | (6.05 6.055 6.06) | (6.01 6.1) | |
MH | (42 45 48) | (12 66) | (0.11 0.12 0.13) | (0.01 0.19) | (4.2 4.5 4.6) | (3 6.8) | (6.06 6.065 6.07) | (6.01 6.1) | |
H | (48 51 54) | (12 66) | (0.13 0.14 0.15) | (0.01 0.19) | (4.5 4.9 5.347) | (3 6.8) | (6.07 6.075 6.08) | (6.01 6.1) | |
VH | (54 57 60) | (12 66) | (0.15 0.16 0.17) | (0.01 0.19) | (5.2 5.6 5.8) | (3 6.8) | (6.08 6.085 6.09) | (6.01 6.1) | |
VVH | (60 63 66) | (12 66) | (0.17 0.18 0.19) | (0.01 0.19) | (5.8 6.4 6.8) | (3 6.8) | (6.09 6.095 6.1) | (6.01 6.1) |
Hole Number | Cutting Speed | Feed Rate | Surface Roughness | Hole Size | ||||
---|---|---|---|---|---|---|---|---|
Experimental Values | Fuzzy Results | % Error | Experimental Values | Fuzzy Results | % Error | |||
1 | 19 | 0.04 | 3.457 | 3.517 | −1.736 | 6.036 | 6.025 | 0.182 |
2 | 19 | 0.08 | 3.718 | 3.774 | −1.506 | 6.044 | 6.038 | 0.101 |
3 | 19 | 0.14 | 4.344 | 4.622 | −6.400 | 6.055 | 6.057 | −0.035 |
4 | 38 | 0.04 | 3.676 | 3.888 | −5.767 | 6.039 | 6.039 | −0.003 |
5 | 38 | 0.08 | 4.126 | 4.136 | −0.242 | 6.048 | 6.050 | −0.028 |
6 | 38 | 0.14 | 4.626 | 4.745 | −2.572 | 6.060 | 6.066 | −0.092 |
7 | 57 | 0.04 | 4.566 | 4.728 | −3.548 | 6.048 | 6.055 | −0.116 |
8 | 57 | 0.08 | 4.990 | 4.962 | 0.561 | 6.061 | 6.065 | −0.064 |
9 | 57 | 0.14 | 5.724 | 5.170 | 9.679 | 6.075 | 6.080 | −0.082 |
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Aamir, M.; Tu, S.; Tolouei-Rad, M.; Giasin, K.; Vafadar, A. Optimization and Modeling of Process Parameters in Multi-Hole Simultaneous Drilling Using Taguchi Method and Fuzzy Logic Approach. Materials 2020, 13, 680. https://doi.org/10.3390/ma13030680
Aamir M, Tu S, Tolouei-Rad M, Giasin K, Vafadar A. Optimization and Modeling of Process Parameters in Multi-Hole Simultaneous Drilling Using Taguchi Method and Fuzzy Logic Approach. Materials. 2020; 13(3):680. https://doi.org/10.3390/ma13030680
Chicago/Turabian StyleAamir, Muhammad, Shanshan Tu, Majid Tolouei-Rad, Khaled Giasin, and Ana Vafadar. 2020. "Optimization and Modeling of Process Parameters in Multi-Hole Simultaneous Drilling Using Taguchi Method and Fuzzy Logic Approach" Materials 13, no. 3: 680. https://doi.org/10.3390/ma13030680
APA StyleAamir, M., Tu, S., Tolouei-Rad, M., Giasin, K., & Vafadar, A. (2020). Optimization and Modeling of Process Parameters in Multi-Hole Simultaneous Drilling Using Taguchi Method and Fuzzy Logic Approach. Materials, 13(3), 680. https://doi.org/10.3390/ma13030680