Experimental Optimization of Nimonic 263 Laser Cutting Using a Particle Swarm Approach
Abstract
:1. Introduction
2. Literature Review
3. Experiments
4. Methodology for the Process Parameters’ Design
4.1. Analysis of Experimental Results
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- For the responses Ra, Rms, and PV, all four process parameters are significant.
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- For the response Kd, the following process parameters are significant: Np, p, and v.
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- For the response Kt, the following parameters are significant: f, p, and v.
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- For the response HV, only parameter f is significant.
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- For the response G, the following parameters are significant: Np, f, and p.
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- Parameter f is significant for all responses except for Kd;
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- Parameter P is significant for all responses except for HV;
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- Parameter Np is significant for all response except for Kt and HV;
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- Parameter v is significant for all responses except for HV and G.
4.2. Process Modeling
4.3. Process Optimization
4.3.1. PSO-Based Process Optimization
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- The initial swarm: While a majority of studies use a random initial swarm, it has been proven that the benefits of initializing particles to good positions could be significant [46]. However, some authors claim that, in contrast to the other metaheuristic methods, the initial swarm does not significantly affect the PSO accuracy. In this study, two options are tested: (a) a randomly generated initial swarm; (b) an initial swarm seeded in the vicinity of the solution that yielded the highest process measure in the experiment (Table 4).
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- The swarm size can take different values from 20 to 40, or up to 100 for very complex problems with a large number of variables. The proposed swarm size is 2n to 5n [47]; n is the number of process parameters in this case. It has been noted that a large swarm size significantly improves the success rate of the algorithm [44]. Since there are four cutting parameters analyzed in this study, the following swarm sizes are tested: 8, 20, and 50.
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- Inertia weight is used to restrict the particle velocity, since a particle could miss out on a good solution due to an excessively large velocity. This parameter has rarely been discussed in the literature. Pant [47] suggested the range [0.4; 0.9] for moderately sized problems with a number of variables from 2 to 20. The following inertia weight ranges are tested: [0.1; 1.1], [0.4; 0.9], [0.5; 2.5], and [1.0.; 5.0].
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- Typically, learning factors c1 and c2 are equal, and have values from 0 to 4. For moderately sized problems, it has been suggested to use c1 = c2 = 2.0 [47]. Since premature convergence is a major weakness of PSO, velocity reduction is recommended to improve the probability of obtaining a global optimum [44]. Therefore, the following values are tested: c1 = c2 = 0.1; c1 = c2 = 0.5; c1 = c2 = 2.0; c1 = c2 = 5, and c1 = 0.7, c2 = 1.5.
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- The algorithm termination usually refers to the specified number of iterations, which typically varies from a few hundred up to a few thousand. In this study, the algorithm terminates when it accomplishes 5000 iterations or when the objective function change over the last 100 iterations is less than 10−9, whichever is earlier.
4.3.2. SA-Based Process Optimization
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- The starting, i.e., initial point is placed near the best solution from the experiment.
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- Initial temperature values of 100 °C and 500 °C are tested.
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- The Boltzmann annealing function and fast annealing function are adopted for the annealing function.
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- For the temperature function, the Boltzmann and the fast temperature functions are tested.
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- The following combinations of reannealing interval and initial temperature are used: [10; 100], [10; 500], [100; 100], [100; 500].
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- The same termination condition as for PSO is used.
5. Experimental Validation and Discussion
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Element | C | Si | Mn | Al | Co | Cr | Cu | Fe | Mo | Ti | Ni |
---|---|---|---|---|---|---|---|---|---|---|---|
% | 0.06 | 0.30 | 0.50 | 0.50 | 20.00 | 20.00 | 0.10 | 0.50 | 5.90 | 2.20 | 49.94 |
Laser Beam Power | 2800 W |
---|---|
Polarization | circular |
Speed | 6000 mm/min |
Pulse Frequency | 2500 Hz |
Assisting Gas | Nitrogen |
Pressure of Assisting Gas | 20 bar |
Responses | Unit | Symbol | Required Value | Response Type in SNR Analysis |
---|---|---|---|---|
Kerf deviation | mm | Kd | Minimal value | STB |
Kerf tapper | ° | Kt | Minimal value | STB |
Microhardness | HV1 | HV | Maximal value | LTB |
Grate | - | G | Minimal value | STB |
Roughness | µm | Ra | Minimal value | STB |
Roughness root mean square | µm | Rms | Minimal value | STB |
Roughness peak-to-valley | - | PV | Minimal value | STB |
Process Parameters | Unit | Symbol | Levels | ||
---|---|---|---|---|---|
1 | 2 | 3 | |||
Nitrogen pressure | bar | Np | 4 | 8 | 12 |
Focus position | - | f | 1 (on the top of the material) | 2 (on the bottom of the material) | 3 (0.5 mm in front of the material) |
Laser power | W | P | 1400 | 2100 | 2800 |
Cutting speed | mm/min | v | 4000 | 4500 | 5000 |
No. | Parameter Levels | Responses | Principal Component Scores Yj(k) (j = 1, … 7; k = 1, … 18) | γk (k = 1, … 18) | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Np | f | P | v | Kd | Kt | HV | G | Ra | Rms | PV | Y1(k) | Y2(k) | Y3(k) | Y4(k) | Y5(k) | Y6(k) | Y7(k) | ||
1 | 1 | 1 | 1 | 1 | 0.063 | 1.13 | 235.2 | 0 | 8.5 | 10.7 | 104.9 | 0.51 | −0.57 | −0.31 | 0.04 | 0.24 | 0.06 | −0.11 | 0.6974 |
2 | 1 | 2 | 2 | 2 | 0.057 | 0.97 | 209.7 | 0 | 8.6 | 10.7 | 106.3 | 0.25 | −0.80 | −0.65 | −0.40 | 0.22 | −0.20 | −0.09 | 0.6932 |
3 | 1 | 3 | 3 | 3 | 0.077 | 1.20 | 219.4 | 0 | 9.5 | 11.4 | 190.6 | 0.75 | −0.38 | −0.82 | −0.46 | 0.61 | 0.09 | −0.15 | 0.5799 |
4 | 2 | 1 | 2 | 3 | 0.047 | 0.90 | 236.3 | 1 | 5.9 | 7.4 | 159.6 | 0.52 | −0.11 | 0.38 | −0.76 | 0.57 | −0.18 | −0.10 | 0.7042 |
5 | 2 | 2 | 3 | 1 | 0.123 | 1.15 | 219.6 | 1 | 10.5 | 11.8 | 158.1 | 1.33 | −1.14 | −0.11 | −1.09 | 0.17 | 0.10 | −0.13 | 0.4965 |
6 | 2 | 3 | 1 | 2 | 0.093 | 0.87 | 240.6 | 0 | 9.5 | 12.0 | 209.7 | 0.83 | 0.11 | −0.68 | −0.45 | 0.29 | 0.11 | −0.05 | 0.6427 |
7 | 3 | 1 | 3 | 2 | 0.127 | 1.40 | 251.5 | 1 | 13.4 | 18.4 | 183.1 | 2.26 | −0.79 | −0.08 | −0.48 | 0.29 | −0.06 | −0.12 | 0.4641 |
8 | 3 | 2 | 1 | 3 | 0.073 | 0.57 | 234.9 | 0 | 5.9 | 11.0 | 198.5 | 0.36 | 0.25 | −0.57 | −0.52 | 0.23 | −0.05 | −0.20 | 0.7272 |
9 | 3 | 3 | 2 | 1 | 0.057 | 0.90 | 230.4 | 0 | 5.2 | 6.3 | 106.6 | 0.07 | −0.40 | −0.22 | −0.16 | 0.18 | 0.09 | −0.15 | 0.8744 |
… | |||||||||||||||||||
18 | 3 | 3 | 2 | 1 | 0.058 | 0.91 | 231.0 | 0 | 5.3 | 6.3 | 107.0 | 0.09 | −0.40 | −0.22 | −0.15 | 0.18 | 0.10 | −0.14 | 0.8672 |
ANN Topology | 4-10-1 | 4-12-1 | 4-15-1 | 4-16-1 | 4-17-1 | 4-18-1 | 4-20-1 |
---|---|---|---|---|---|---|---|
MSE | 2.68 × 10−5 | 4.22 × 10−6 | 3.48 × 10−6 | 1.85 × 10−6 | 1.51 × 10−6 | 8.45 × 10−6 | 1.32 × 10−5 |
R for training data | 0.97 | 0.97 | 0.98 | 0.98 | 0.99 | 0.99 | 0.98 |
R for all data | 0.99 | 0.99 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
Optimization Algorithm | PSO with a Random Initial Population | PSO with a Defined Initial Population | SA |
---|---|---|---|
The range of the obtained process measure γ | 0.894012 ÷ 0.900825 | 0.893701 ÷ 0.900825 | 0.890861 ÷ 0.900762 |
The best process measure γ | 0.900825 | 0.900825 | 0.900762 |
The optimal process parameters setting that corresponds to the best γ | [14; 3; 2034; 4000] | [14; 3; 2034; 4000] | [14; 3; 2039; 4000] |
The number of iterations at which the best process measure is reached | 30 ÷ 70 | 6 ÷ 30 | 40 ÷ 1520 |
The total number of iterations performed by the algorithm | 121 ÷ 341 | 105 ÷ 291 | 2027 ÷ 3530 |
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Sibalija, T.; Petronic, S.; Milovanovic, D. Experimental Optimization of Nimonic 263 Laser Cutting Using a Particle Swarm Approach. Metals 2019, 9, 1147. https://doi.org/10.3390/met9111147
Sibalija T, Petronic S, Milovanovic D. Experimental Optimization of Nimonic 263 Laser Cutting Using a Particle Swarm Approach. Metals. 2019; 9(11):1147. https://doi.org/10.3390/met9111147
Chicago/Turabian StyleSibalija, Tatjana, Sanja Petronic, and Dubravka Milovanovic. 2019. "Experimental Optimization of Nimonic 263 Laser Cutting Using a Particle Swarm Approach" Metals 9, no. 11: 1147. https://doi.org/10.3390/met9111147