Multi-Objective Optimization in Ultrasonic Polishing of Silicon Carbide via Taguchi Method and Grey Relational Analysis
Abstract
:1. Introduction
2. Materials and Methods
2.1. Consumables and Equipment
2.2. Taguchi Experimental Scheme and Implementation
2.3. Optimization Procedures
3. Results and Discussion
3.1. Effect of Process Parameters on Response Characteristics
3.2. Multi-Response Optimization
3.2.1. Calculation of SNRs
3.2.2. Calculation of GRC and Response Weights
3.3. Optimal Combination Verification
4. Conclusions
- The analysis of variance was performed to investigate the effect of selected parameters on polishing characteristics. The influence degree on the surface roughness is abrasive size > preloading force > abrasive content > spindle speed > feed rate. The best process combination on the surface roughness is the abrasive content of 2 wt%, abrasive size of 0.5 μm, preloading force of 60 N, spindle speed of 14,000 rpm, and feed rate of 3 mm/s. The influence order on the material removal rate is spindle speed > abrasive size > feed rate > preloading force > abrasive content. The best process combination on the material removal rate is the abrasive content of 14 wt%, abrasive size of 2.5 μm, preloading force of 80 N, spindle speed of 8000 rpm, and feed rate of 1 mm/s.
- The Taguchi–GRA optimization method was operated successfully, and the best process combination combining material removal rate and surface roughness is the abrasive content of 14 wt%, abrasive size of 2.5 μm, preloading force of 80 N, spindle speed of 8000 rpm, and feed rate of 1 mm/s. The optimized workpiece showed improvements in surface roughness and material removal rate by 7.14% and 28.34%, respectively, compared to the group with the best GRG.
- The Taguchi–GRA method provides a more scientific approach for evaluating the comprehensive performance of precision polishing. The research findings have essential relevance for ultra-precision polishing of optical ceramic materials, especially silicon carbide.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Properties | Material Type | ||
---|---|---|---|
SiC | Diamond | Polyurethane | |
Density (g/cm3) | 3.12 | 3.52 | 0.49 |
Young’s modulus (GPa) | 410 | 1000 | 2.29 × 10−3 |
Poisson ratio | 0.16 | 0.07 | 0.47 |
Hardness (GPa) | 28.4–33.2 | 50 | 72 (Shore A) |
Fracture toughness (Mpa·m1/2) | 4.5 | - | - |
No. | Factors | ||||
---|---|---|---|---|---|
A: Abrasive Content Wa (wt%) | B: Abrasive Size Da (μm) | C: Preloading Force F0 (N) | D: Spindle Speed n (rpm) | E: Feed Rate vw (mm/s) | |
1 | 2 | 0.5 | 20 | 2000 | 1 |
2 | 2 | 1.5 | 40 | 5000 | 1.5 |
3 | 2 | 2.5 | 60 | 8000 | 2 |
4 | 2 | 3.5 | 80 | 11,000 | 2.5 |
5 | 2 | 7 | 100 | 14,000 | 3 |
6 | 6 | 0.5 | 40 | 8000 | 2.5 |
7 | 6 | 1.5 | 60 | 11,000 | 3 |
8 | 6 | 2.5 | 80 | 14,000 | 1 |
9 | 6 | 3.5 | 100 | 2000 | 1.5 |
10 | 6 | 7 | 20 | 5000 | 2 |
11 | 10 | 0.5 | 60 | 14,000 | 1.5 |
12 | 10 | 1.5 | 80 | 2000 | 2 |
13 | 10 | 2.5 | 100 | 5000 | 2.5 |
14 | 10 | 3.5 | 20 | 8000 | 3 |
15 | 10 | 7 | 40 | 11,000 | 1 |
16 | 14 | 0.5 | 80 | 5000 | 3 |
17 | 14 | 1.5 | 100 | 8000 | 1 |
18 | 14 | 2.5 | 20 | 11,000 | 1.5 |
19 | 14 | 3.5 | 40 | 14,000 | 2 |
20 | 14 | 7 | 60 | 2000 | 2.5 |
21 | 18 | 0.5 | 100 | 11,000 | 2 |
22 | 18 | 1.5 | 20 | 14,000 | 2.5 |
23 | 18 | 2.5 | 40 | 2000 | 3 |
24 | 18 | 3.5 | 60 | 5000 | 1 |
25 | 18 | 7 | 80 | 8000 | 1.5 |
Parameters | Value |
---|---|
Ultrasonic amplitude A (μm) | 10 |
Ultrasonic frequency f (kHz) | 25 |
Polishing tool diameter Dt (mm) | 10 |
Polishing time t (min) | 20 |
Polishing distance d (mm) | 10 |
No. | Response Characteristics | |
---|---|---|
Surface Roughness (nm) | Material Removal Rate (μm2/min) | |
1 | 17 | 1588.15 |
2 | 16 | 1824.73 |
3 | 14 | 6564.07 |
4 | 16 | 6408.33 |
5 | 19 | 4442.52 |
6 | 16 | 4418.63 |
7 | 12 | 4702.45 |
8 | 17 | 6451.84 |
9 | 18 | 3219.67 |
10 | 25 | 2896.72 |
11 | 13 | 5716.37 |
12 | 17 | 2781.35 |
13 | 20 | 6126.36 |
14 | 22 | 2759.52 |
15 | 22 | 6020.24 |
16 | 11 | 2139.70 |
17 | 17 | 7432.72 |
18 | 22 | 6228.33 |
19 | 21 | 7947.56 |
20 | 24 | 2438.75 |
21 | 15 | 3197.98 |
22 | 15 | 2282.79 |
23 | 21 | 2217.88 |
24 | 21 | 5975.30 |
25 | 25 | 7741.11 |
Source | DF | Adj SS | Adj MS | F-Values | Contribution |
---|---|---|---|---|---|
A | 4 | 30.16 | 7.54 | 0.93 | 8.90% |
B | 4 | 238.16 | 59.54 | 7.31 | 69.95% |
C | 4 | 40.56 | 10.14 | 1.25 | 11.96% |
D | 4 | 20.16 | 5.04 | 0.62 | 5.93% |
E | 4 | 10.96 | 2.74 | 0.34 | 3.25% |
Error | 4 | 32.56 | 8.14 | - | - |
Total | 24 | 372.56 | - | - | - |
Source | DF | Adj SS | Adj MS | F-Values | Contribution |
---|---|---|---|---|---|
A | 4 | 3,766,513 | 941,628 | 0.24 | 4.27% |
B | 4 | 16,589,875 | 4,147,469 | 1.08 | 19.22% |
C | 4 | 13,298,819 | 3,324,705 | 0.87 | 15.48% |
D | 4 | 38,784,722 | 9,696,180 | 2.52 | 44.84% |
©E | 4 | 13,965,735 | 3,491,434 | 0.91 | 16.19% |
Error | 4 | 15,373,706 | 3,843,427 | - | - |
Total | 24 | 101,779,369 | - | - | - |
No. | SNR of Response Characteristics | |
---|---|---|
Surface Roughness | Material Removal Rate | |
1 | −24.6090 | 64.0178 |
2 | −24.0824 | 65.2240 |
3 | −22.9226 | 76.3435 |
4 | −24.0824 | 76.1349 |
5 | −25.5751 | 72.9526 |
6 | −24.0824 | 72.9058 |
7 | −21.5836 | 73.4465 |
8 | −24.6090 | 76.1937 |
9 | −25.1055 | 70.1562 |
10 | −27.9588 | 69.2381 |
11 | −22.2789 | 75.1424 |
12 | −24.6090 | 68.8851 |
13 | −26.0206 | 75.7441 |
14 | −26.8485 | 68.8167 |
15 | −26.8485 | 75.5923 |
16 | −20.8279 | 66.6070 |
17 | −24.6090 | 77.4230 |
18 | −26.8485 | 75.8874 |
19 | −26.4444 | 78.0047 |
20 | −27.6042 | 67.7434 |
21 | −23.5218 | 70.0975 |
22 | −23.5218 | 67.1693 |
23 | −26.4444 | 66.9188 |
24 | −26.4444 | 75.5272 |
25 | −27.9588 | 77.7761 |
No. | Normalized SNR | GRC | GRG | ||
---|---|---|---|---|---|
Surface Roughness | Material Removal Rate | Surface Roughness | Material Removal Rate | ||
1 | 0.4698 | 0.0000 | 0.4853 | 0.3333 | 0.4015 |
2 | 0.5436 | 0.0862 | 0.5228 | 0.3537 | 0.4295 |
3 | 0.7063 | 0.8812 | 0.6299 | 0.8081 | 0.7282 |
4 | 0.5436 | 0.8663 | 0.5228 | 0.7890 | 0.6697 |
5 | 0.3343 | 0.6388 | 0.4289 | 0.5806 | 0.5126 |
6 | 0.5436 | 0.6354 | 0.5228 | 0.5783 | 0.5534 |
7 | 0.8940 | 0.6741 | 0.8251 | 0.6054 | 0.7039 |
8 | 0.4698 | 0.8705 | 0.4853 | 0.7943 | 0.6558 |
9 | 0.4001 | 0.4389 | 0.4546 | 0.4712 | 0.4638 |
10 | 0.0000 | 0.3732 | 0.3333 | 0.4437 | 0.3943 |
11 | 0.7965 | 0.7954 | 0.7108 | 0.7096 | 0.7101 |
12 | 0.4698 | 0.3480 | 0.4853 | 0.4340 | 0.4570 |
13 | 0.2718 | 0.8384 | 0.4071 | 0.7557 | 0.5995 |
14 | 0.1557 | 0.3431 | 0.3719 | 0.4322 | 0.4052 |
15 | 0.1557 | 0.8275 | 0.3719 | 0.7435 | 0.5770 |
16 | 1.00 | 0.19 | 1.0000 | 0.3803 | 0.6580 |
17 | 0.47 | 0.96 | 0.4853 | 0.9232 | 0.7270 |
18 | 0.16 | 0.85 | 0.3719 | 0.7676 | 0.5903 |
19 | 0.21 | 1.00 | 0.3883 | 1.0000 | 0.7259 |
20 | 0.05 | 0.27 | 0.3448 | 0.4053 | 0.3782 |
21 | 0.62 | 0.43 | 0.5696 | 0.4693 | 0.5143 |
22 | 0.62 | 0.23 | 0.5696 | 0.3923 | 0.4717 |
23 | 0.21 | 0.21 | 0.3883 | 0.3868 | 0.3875 |
24 | 0.21 | 0.82 | 0.3883 | 0.7384 | 0.5815 |
25 | 0.00 | 0.98 | 0.3333 | 0.9683 | 0.6837 |
Source | DF | Adj SS | Adj MS | F-Values | Contribution |
---|---|---|---|---|---|
A | 4 | 0.02216 | 0.00554 | 0.37 | 7.33% |
B | 4 | 0.01884 | 0.004709 | 0.31 | 6.14% |
C | 4 | 0.10021 | 0.025052 | 1.66 | 32.87% |
D | 4 | 0.15115 | 0.037787 | 2.51 | 49.70% |
E | 4 | 0.01211 | 0.003027 | 0.2 | 3.96% |
Error | 4 | 0.06027 | 0.015067 | - | - |
Total | 24 | 0.36473 | - | - | - |
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Chen, X.; Xu, S.; Meng, F.; Yu, T.; Zhao, J. Multi-Objective Optimization in Ultrasonic Polishing of Silicon Carbide via Taguchi Method and Grey Relational Analysis. Materials 2023, 16, 5673. https://doi.org/10.3390/ma16165673
Chen X, Xu S, Meng F, Yu T, Zhao J. Multi-Objective Optimization in Ultrasonic Polishing of Silicon Carbide via Taguchi Method and Grey Relational Analysis. Materials. 2023; 16(16):5673. https://doi.org/10.3390/ma16165673
Chicago/Turabian StyleChen, Xin, Shucong Xu, Fanwei Meng, Tianbiao Yu, and Ji Zhao. 2023. "Multi-Objective Optimization in Ultrasonic Polishing of Silicon Carbide via Taguchi Method and Grey Relational Analysis" Materials 16, no. 16: 5673. https://doi.org/10.3390/ma16165673