Buckling Defect Optimization of Constrained Ring Rolling of Thin-Walled Conical Rings with Inner High Ribs Combining Response Surface Method with FEM
Abstract
:1. Introduction
2. Optimization Method
2.1. Establishment of Finite Element Model of Constrained Ring Rolling of AATWCRIHR
2.2. Evaluation Criteria of Buckling Defect
2.3. Determination of Experimental Scheme
3. Results and Analysis
3.1. Orthogonal Experimental Analysis
3.2. Orthogonal Experimental Level Analysis
3.3. Establishment of Response Surface Model
0.0035 × A × C + 0.0019 × B × C + 0.1262 × A2 − 0.9025 × B2 + 0.0185 × C2
3.4. Analysis of Variance (ANOVA)
3.5. RSM Analysis
4. Verification Model
5. Conclusions
- The degree of influence on the buckling defect is the width of the middle rib, the wall thickness, and the height of the middle rib, in that order.
- The buckling area is the smallest and the degree of the buckling defect on the back of the middle rib is the lowest when the width of the middle rib is 24 mm, the wall thickness is 6 mm, and the height of the middle rib is 51 mm.
- When the width of the middle rib is larger, the degree of the buckling defect becomes more significant with the decrease in wall thickness. When the width of the middle rib is smaller, the thickness of the wall has little influence on the buckling defect, and the degree of the buckling defect is light.
- The quantitative representation of the buckling defect proposed using the buckling profile S is feasible, and the response surface model can predict the degree of the buckling defect at a given geometry dimension of the middle rib and the wall thickness of the conical ring billet by verification.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter | Tensile Strength (MPa) | Yield Strength (MPa) | Elastic Modulus (GPa) | Poisson’s Ratio | Thermal Conductivity (W × m−1 × K−1) | Specific Heat Capacity (J × Kg−1 K−1) |
---|---|---|---|---|---|---|
Value | 175 | 75 | 73 | 0.33 | 180.2 | 901 |
Symbol | Factors | Level 1 | Level 2 | Level 3 | Level 4 |
---|---|---|---|---|---|
A | Width of rib/b2 (mm) | 24 | 30 | 35 | 40 |
B | Thickness of wall/t (mm) | 3 | 4 | 5 | 6 |
C | Height of rib/h2 (mm) | 41 | 46 | 51 | 56 |
Experiment NO. | A (mm) | B (mm) | C (mm) | S (mm2) |
---|---|---|---|---|
1 | 24 | 3 | 41 | 0.58 |
2 | 24 | 4 | 56 | 0.85 |
3 | 24 | 5 | 51 | 0.87 |
4 | 24 | 6 | 46 | 0.44 |
5 | 30 | 3 | 46 | 0.57 |
6 | 30 | 4 | 56 | 0.83 |
7 | 30 | 5 | 51 | 0.82 |
8 | 30 | 6 | 41 | 0.83 |
9 | 35 | 3 | 51 | 11.35 |
10 | 35 | 4 | 41 | 10.85 |
11 | 35 | 5 | 46 | 7.75 |
12 | 35 | 6 | 56 | 3.92 |
13 | 40 | 3 | 56 | 26.30 |
14 | 40 | 4 | 46 | 25.32 |
15 | 40 | 5 | 41 | 22.42 |
16 | 40 | 6 | 51 | 12.75 |
K1 | 0.68 | 9.70 | 8.67 | |
K2 | 0.76 | 9.46 | 8.52 | |
K3 | 8.47 | 7.69 | 6.44 | |
K4 | 21.70 | 4.48 | 7.98 | |
Range Rs | −21.01 | −5.21 | −2.23 |
Source | Sum of Squares | DOF | Mean Square | F-Value | p-Value | Degree of Significance |
---|---|---|---|---|---|---|
Model | 1316.65 | 9 | 146.29 | 104.82 | <0.0001 | significant |
A | 926.77 | 1 | 926.77 | 664.04 | <0.0001 | |
B | 47.21 | 1 | 47.21 | 33.83 | 0.0011 | |
C | 10.96 | 1 | 10.96 | 7.85 | 0.0311 | |
AB | 38.32 | 1 | 38.32 | 27.46 | 0.0019 | |
AC | 0.073 | 1 | 0.073 | 0.052 | 0.8269 | |
BC | 1.206 × 10−3 | 1 | 1.206 × 10−3 | 8.640 × 10−4 | 0.9775 | |
A2 | 211.28 | 1 | 211.28 | 151.38 | <0.0001 | |
B2 | 4.57 | 1 | 4.57 | 3.27 | 0.1205 | |
C2 | 3.40 | 1 | 3.40 | 2.44 | 0.1695 | |
Residual error | 8.37 | 6 | 1.40 | |||
Correlation coefficient R2 | Modified coefficient of determination Radj2 | Model prediction coefficient Rpred2 | S/N Ratio | |||
0.9937 | 0.9842 | 0.9355 | 28.303 |
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Feng, W.; Zhao, P. Buckling Defect Optimization of Constrained Ring Rolling of Thin-Walled Conical Rings with Inner High Ribs Combining Response Surface Method with FEM. Metals 2024, 14, 378. https://doi.org/10.3390/met14040378
Feng W, Zhao P. Buckling Defect Optimization of Constrained Ring Rolling of Thin-Walled Conical Rings with Inner High Ribs Combining Response Surface Method with FEM. Metals. 2024; 14(4):378. https://doi.org/10.3390/met14040378
Chicago/Turabian StyleFeng, Wei, and Peng Zhao. 2024. "Buckling Defect Optimization of Constrained Ring Rolling of Thin-Walled Conical Rings with Inner High Ribs Combining Response Surface Method with FEM" Metals 14, no. 4: 378. https://doi.org/10.3390/met14040378