Multi-Objective Optimization of Micro-Milling Parameters—The Trade-Offs between Machining Quality, Efficiency, and Sustainability in the Fabrication of Thin-Walled Microstructures
Abstract
:1. Introduction
2. Materials and Methods
2.1. Power Consumption Modeling
2.1.1. Power Consumption Modeling in Feed and Spindle Subsystems
2.1.2. Material Removal Power Modeling
2.2. Description of the Multi-Objective Optimization Problem
2.3. Experimental Design
3. Results and Discussions
4. Conclusions
- (1)
- The power consumption characteristics of the micro-milling process were analyzed, and a process-parameter-based power consumption model was established. The analysis revealed that the power consumption of non-machining feed motion exhibits a quadratic relationship with the feed rate, while the non-machining spindle power consumption shows a quadratic relationship with the spindle speed. The spindle speed exerts the greatest influence on the variable power consumption.
- (2)
- The coefficient between SCE and MRR was −0.793, which indicates that enhancing machining efficiency can simultaneously improve machining sustainability.
- (3)
- Among the three indicators characterizing machining quality, surface roughness and surface fractal dimension exhibited a significant negative correlation (with a correlation coefficient of −0.832). However, their correlations with dimensional error were relatively small, being 0.57 and −0.628, respectively. After performing PCA, the variance extraction percentages for Sa, Ds, and De all exceeded 50%, indicating a good level of information condensation.
- (4)
- The optimization results of the process parameters demonstrate that the NSGA-III-based optimization method yields a better trade-off between machinability and sustainability, indicating that NSGA-III exhibits superior performance in handling multi-objective optimization problems and can obtain globally optimal parameters. The optimal combination of micro-milling parameters was n = 28,800 rpm, fz = 2.6 μm/t, and ap = 62 μm.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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f (mm/min) | n (rpm) | ap (μm) |
---|---|---|
20, 120, 220, 320, and 420 | 0 | 0 |
0 | 10,000, 15,000, 20,000, 25,000, 30,000, 35,000, 40,000, and 45,000 | 0 |
Symbol | Process Parameters | Units | Level | |||
---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | |||
A | Spindle speed (n) | r/min | 15,000 | 25,000 | 35,000 | 45,000 |
B | Axial depth of cut (ap) | μm | 50 | 60 | 100 | 150 |
C | Feed per tooth (fz) | μm/tooth | 0.5 | 1.5 | 2.5 | 3.5 |
No. | Symbol | Sa (nm) | De (μm) | Ds | SCE (kJ/mm3) | MRR (mm3/min) | Level | ||
---|---|---|---|---|---|---|---|---|---|
A | B | C | |||||||
1 | A1B1C1 | 45 | 1.3 | 2.5110 | 15.94 | 0.60 | 15,000 | 50 | 0.5 |
2 | A1B2C2 | 56 | 2.8 | 2.4620 | 4.50 | 2.16 | 15,000 | 60 | 1.5 |
3 | A1B3C3 | 60 | 2.9 | 2.4468 | 1.67 | 6.00 | 15,000 | 100 | 2.5 |
4 | A1B4C4 | 143 | 4.1 | 2.4108 | 0.82 | 12.60 | 15,000 | 150 | 3.5 |
5 | A2B1C2 | 48 | 3.2 | 2.4960 | 15.50 | 1.20 | 20,000 | 60 | 0.5 |
6 | A2B2C1 | 54 | 2.2 | 2.4730 | 6.15 | 3.00 | 20,000 | 50 | 1.5 |
7 | A2B3C4 | 185 | 4.3 | 2.3663 | 1.28 | 15.00 | 20,000 | 150 | 2.5 |
8 | A2B4C3 | 121 | 4.4 | 2.3903 | 1.38 | 14.00 | 20,000 | 100 | 3.5 |
9 | A3B1C3 | 57 | 2.8 | 2.4565 | 10.27 | 2.80 | 25,000 | 100 | 0.5 |
10 | A3B2C4 | 133 | 4.6 | 2.4478 | 2.31 | 12.60 | 25,000 | 150 | 1.5 |
11 | A3B3C1 | 58 | 2.7 | 2.4500 | 4.15 | 7.00 | 25,000 | 50 | 2.5 |
12 | A3B4C2 | 99 | 3.5 | 2.4346 | 2.49 | 11.76 | 25,000 | 60 | 3.5 |
13 | A4B1C4 | 60 | 2.3 | 2.4441 | 8.22 | 5.40 | 30,000 | 150 | 0.5 |
14 | A4B2C3 | 85 | 4.7 | 2.4346 | 4.09 | 10.80 | 30,000 | 100 | 1.5 |
15 | A4B3C2 | 90 | 3.8 | 2.4291 | 4.10 | 10.80 | 30,000 | 60 | 2.5 |
16 | A4B4C1 | 66 | 5.7 | 2.4391 | 3.52 | 12.60 | 30,000 | 50 | 3.5 |
Feed Unit | Spindle Unit | ||||
---|---|---|---|---|---|
R2 | R2-pre | R2-adj | R2 | R2-pre | R2-adj |
99.21% | 94.42% | 98.43% | 99.92% | 99.82% | 98.89% |
No. | Ptatal (W) | Pb (W) | Ps (W) | Pf (W) | Pm (W) |
---|---|---|---|---|---|
(Measured) | (Measured) | (Calculated) | (Calculated) | (Calculated) | |
1 | 645.4 | 486 | 127 | 1.9 | 33.5 |
2 | 648.1 | 2.1 | 36.0 | ||
3 | 653.3 | 2.4 | 40.9 | ||
4 | 659.3 | 2.7 | 46.6 | ||
5 | 793.9 | 271 | 2.4 | 36.5 | |
6 | 795.7 | 2.0 | 34.7 | ||
7 | 802.5 | 3.8 | 44.7 | ||
8 | 806.9 | 3.0 | 46.9 | ||
9 | 965.2 | 440 | 3.8 | 35.4 | |
10 | 969.0 | 5.4 | 39.6 | ||
11 | 970.7 | 2.1 | 42.6 | ||
12 | 976.2 | 2.7 | 45.5 | ||
13 | 1221.4 | 692 | 7.4 | 40.0 | |
14 | 1202.3 | 4. 9 | 38.7 | ||
15 | 1224.0 | 3.1 | 42.9 | ||
16 | 1228.5 | 2.1 | 46.4 |
R2 | R2-adj | R2-pre | AIC | BIC | |
---|---|---|---|---|---|
Exponential model | 0.8589 | 0.8236 | 0.7300 | −34.32 | −36.46 |
Polynomial model | 0.9185 | 0.8641 | 0.6755 | 89.53 | 75.14 |
n (rpm) | fz (μm/t) | ap (μm) | |
---|---|---|---|
Rj | 572.9 | 8.7 | 6.2 |
Ranking | 1 | 2 | 3 |
Sa | Ds | De | |||
---|---|---|---|---|---|
R2 | R2-adj | R2 | R2-adj | R2 | R2-adj |
77.71% | 72.14% | 81.27% | 76.59% | 67.47% | 59.33% |
Sa | Ds | De | |
---|---|---|---|
Sa | 1 | −0.832 | 0.579 |
Ds | −0.832 | 1 | −0.628 |
De | 0.579 | −0.628 | 1 |
Sampling Adequacy KMO Measure | 0.681 | |
---|---|---|
Bartlett’s test of sphericity | Approximate chi-square | 22.351 |
df | 3 | |
Sig. | 0.000 |
Initial Variance | Extracted Variance | |
---|---|---|
Sa | 1.000 | 0.834 |
Ds | 1.000 | 0.867 |
De | 1.000 | 0.665 |
No. | Initial Eigenvalue | Extract Loading Sum of Squares | ||||
---|---|---|---|---|---|---|
Eigenvalue | Initial Variance % | Cumulative Variance % | Eigenvalue | Initial Variance % | Cumulative Variance % | |
1 | 2.366 | 78.851 | 78.851 | 2.366 | 78.851 | 78.851 |
2 | 0.470 | 15.654 | 94.505 | |||
3 | 0.165 | 5.495 | 100.000 |
Sa | Ds | De |
---|---|---|
0.386 | −0.394 | 0.345 |
n | fz | ap | Sa | Ds | De | MRR | SCE | |
---|---|---|---|---|---|---|---|---|
NSGA-II | 17,760 | 3.3 | 98 | 65 | 2.4860 | 3.5 | 9.37 | 0.960 |
MOPSO | 21,000 | 3.2 | 88 | 59 | 2.4980 | 3.6 | 9.46 | 1.110 |
NSGA-III | 28,800 | 2.6 | 62 | 50 | 2.5010 | 2.0 | 9.36 | 1.126 |
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Wang, P.; Bai, Q.; Cheng, K.; Zhao, L.; Zhang, Y. Multi-Objective Optimization of Micro-Milling Parameters—The Trade-Offs between Machining Quality, Efficiency, and Sustainability in the Fabrication of Thin-Walled Microstructures. Appl. Sci. 2023, 13, 9392. https://doi.org/10.3390/app13169392
Wang P, Bai Q, Cheng K, Zhao L, Zhang Y. Multi-Objective Optimization of Micro-Milling Parameters—The Trade-Offs between Machining Quality, Efficiency, and Sustainability in the Fabrication of Thin-Walled Microstructures. Applied Sciences. 2023; 13(16):9392. https://doi.org/10.3390/app13169392
Chicago/Turabian StyleWang, Peng, Qingshun Bai, Kai Cheng, Liang Zhao, and Yabo Zhang. 2023. "Multi-Objective Optimization of Micro-Milling Parameters—The Trade-Offs between Machining Quality, Efficiency, and Sustainability in the Fabrication of Thin-Walled Microstructures" Applied Sciences 13, no. 16: 9392. https://doi.org/10.3390/app13169392
APA StyleWang, P., Bai, Q., Cheng, K., Zhao, L., & Zhang, Y. (2023). Multi-Objective Optimization of Micro-Milling Parameters—The Trade-Offs between Machining Quality, Efficiency, and Sustainability in the Fabrication of Thin-Walled Microstructures. Applied Sciences, 13(16), 9392. https://doi.org/10.3390/app13169392