Author Contributions
Conceptualization, P.Y.; data curation, P.Y. and T.S.; formal analysis, P.Y. and X.J.; investigation, P.Y., T.S., X.J., X.Q. and W.Z.; methodology, P.Y., T.S., X.J., X.Q. and W.Z.; writing—original draft preparation, P.Y.; writing—review and editing, P.Y., supervision, X.J., W.L., Q.X., X.Q., Y.Y., X.S. and J.Z. All authors have read and agreed to the published version of the manuscript.
Figure 1.
Major steps of data–physics fusion-driven framework.
Figure 1.
Major steps of data–physics fusion-driven framework.
Figure 2.
Casing process flow [
29].
Figure 2.
Casing process flow [
29].
Figure 3.
Simulation flow of shrinkage cavity formation and material loosening defects in a Ti alloy casing.
Figure 3.
Simulation flow of shrinkage cavity formation and material loosening defects in a Ti alloy casing.
Figure 4.
Neural network model. (a) Tanh. (b) ReLU. (c) Model structure.
Figure 4.
Neural network model. (a) Tanh. (b) ReLU. (c) Model structure.
Figure 5.
No.1 and No.5 solidification processes’ isolated liquid region, shrinkage cavity, and loose defects evolution, with solidification time. (a) No.1 sample. (b) No.5 sample.
Figure 5.
No.1 and No.5 solidification processes’ isolated liquid region, shrinkage cavity, and loose defects evolution, with solidification time. (a) No.1 sample. (b) No.5 sample.
Figure 6.
Influence of key process parameters on the number and total volume of shrinkage cavity and loosening.
Figure 6.
Influence of key process parameters on the number and total volume of shrinkage cavity and loosening.
Figure 7.
Correlation test of proposed parameters and simulation results. (a) Pearson relevance. (b) Spearman relevance.
Figure 7.
Correlation test of proposed parameters and simulation results. (a) Pearson relevance. (b) Spearman relevance.
Figure 8.
Regression model of shrinkage cavities’ number and volume with pouring temperature and shell temperature. (a) Shrinkage cavity number. (b) Shrinkage cavity volume.
Figure 8.
Regression model of shrinkage cavities’ number and volume with pouring temperature and shell temperature. (a) Shrinkage cavity number. (b) Shrinkage cavity volume.
Figure 9.
Regression model of shrinkage loosening number and volume with pouring temperature and shell temperature. (a) Count of shrinkage loosening. (b) Shrinkage loosening volume.
Figure 9.
Regression model of shrinkage loosening number and volume with pouring temperature and shell temperature. (a) Count of shrinkage loosening. (b) Shrinkage loosening volume.
Figure 10.
Relationship curves for the effect of key process parameters on shrinkage cavities and loose defects. (a) Count and volume of shrinkage cavity and loosening change with pouring temperature. (b) Count and volume of shrinkage cavity and loosening change with shell temperature. (c) Count and volume of shrinkage cavity and loosening change with pouring time. (d) Shrinkage cavity, shrinkage loosening, and combine average volume vary with pouring temperature. (e) Shrinkage cavity, shrinkage loosening, and combine average volume vary with shell temperature. (f) Shrinkage cavity, shrinkage loosening, and combine average volume vary with pouring time.
Figure 10.
Relationship curves for the effect of key process parameters on shrinkage cavities and loose defects. (a) Count and volume of shrinkage cavity and loosening change with pouring temperature. (b) Count and volume of shrinkage cavity and loosening change with shell temperature. (c) Count and volume of shrinkage cavity and loosening change with pouring time. (d) Shrinkage cavity, shrinkage loosening, and combine average volume vary with pouring temperature. (e) Shrinkage cavity, shrinkage loosening, and combine average volume vary with shell temperature. (f) Shrinkage cavity, shrinkage loosening, and combine average volume vary with pouring time.
Figure 11.
Effect of pouring and shell temperature on the number and total volume of shrinkage cavities. (a) Effect of pouring temperature and shell temperature on the number of shrinkage cavities. (b) Effect of pouring temperature and shell temperature on the volume of shrinkage cavities.
Figure 11.
Effect of pouring and shell temperature on the number and total volume of shrinkage cavities. (a) Effect of pouring temperature and shell temperature on the number of shrinkage cavities. (b) Effect of pouring temperature and shell temperature on the volume of shrinkage cavities.
Figure 12.
Effect of pouring and shell temperature on the number and total volume of shrinkage loosening. (a) Effect of pouring temperature and shell temperature on the number of shrinkage loosening. (b) Effect of pouring temperature and shell temperature on the volume of shrinkage loosening.
Figure 12.
Effect of pouring and shell temperature on the number and total volume of shrinkage loosening. (a) Effect of pouring temperature and shell temperature on the number of shrinkage loosening. (b) Effect of pouring temperature and shell temperature on the volume of shrinkage loosening.
Figure 13.
Effect of pouring temperature and time on the number and total volume of shrinkage cavities. (a) Effect of pouring temperature and pouring time on the number of shrinkage cavities. (b) Effect of pouring temperature and pouring time on the volume of shrinkage cavities.
Figure 13.
Effect of pouring temperature and time on the number and total volume of shrinkage cavities. (a) Effect of pouring temperature and pouring time on the number of shrinkage cavities. (b) Effect of pouring temperature and pouring time on the volume of shrinkage cavities.
Figure 14.
Effect of pouring temperature and time on the number and total volume of shrinkage loosening. (a) Effect of pouring temperature and pouring time on the number of shrinkage loosening. (b) Effect of pouring temperature and pouring time on the volume of shrinkage loosening.
Figure 14.
Effect of pouring temperature and time on the number and total volume of shrinkage loosening. (a) Effect of pouring temperature and pouring time on the number of shrinkage loosening. (b) Effect of pouring temperature and pouring time on the volume of shrinkage loosening.
Figure 15.
Effect of shell temperature and pouring time on the number and total volume of shrinkage cavities. (a) Effect of pouring time and shell temperature on the number of shrinkage cavities. (b) Effect of pouring time and shell temperature on the volume of shrinkage cavities.
Figure 15.
Effect of shell temperature and pouring time on the number and total volume of shrinkage cavities. (a) Effect of pouring time and shell temperature on the number of shrinkage cavities. (b) Effect of pouring time and shell temperature on the volume of shrinkage cavities.
Figure 16.
Effect of shell temperature and pouring time on the number and total volume of shrinkage loosening. (a) Effect of pouring time and shell temperature on the number of shrinkage loosening. (b) Effect of pouring time and shell temperature on the volume of shrinkage loosening.
Figure 16.
Effect of shell temperature and pouring time on the number and total volume of shrinkage loosening. (a) Effect of pouring time and shell temperature on the number of shrinkage loosening. (b) Effect of pouring time and shell temperature on the volume of shrinkage loosening.
Figure 17.
The relationship between key process parameters and average volume after optimization. (a) Effect of pouring temperature on the average volume. (b) Effect of shell temperature on the average volume. (c) Effect of pouring time on the average volume.
Figure 17.
The relationship between key process parameters and average volume after optimization. (a) Effect of pouring temperature on the average volume. (b) Effect of shell temperature on the average volume. (c) Effect of pouring time on the average volume.
Figure 18.
Shrinkage cavity and loosening of pouring channel. (a) Appearance of pouring channel. (b) Internal of pouring channel.
Figure 18.
Shrinkage cavity and loosening of pouring channel. (a) Appearance of pouring channel. (b) Internal of pouring channel.
Figure 19.
Shrinkage cavity and loosening of riser. (a) Appearance of riser. (b) Internal of riser.
Figure 19.
Shrinkage cavity and loosening of riser. (a) Appearance of riser. (b) Internal of riser.
Table 1.
ZTC4 Ti alloy composition content in terms of weight percent (wt%).
Table 1.
ZTC4 Ti alloy composition content in terms of weight percent (wt%).
Elements | Ti | Al | Fe | H | Si | V | C | O | N |
---|
Content | 89.3 | 6.2 | 0.2 | 0.01 | 0.1 | 4 | 0.06 | 0.1 | 0.03 |
Table 2.
ZTC4 Ti alloy thermophysical properties.
Table 2.
ZTC4 Ti alloy thermophysical properties.
Thermal Emissivity (W/m2) | Latent Heat (J/g) | Liquidus (°C) | Solidus (°C) | Critical Solid Fraction | Solidification Coefficient (mm/s1/2) | Shrinkage of Phase Transition | Liquid Shrinkage Degree |
---|
0.13 | 335.62 | 1650 | 1600 | 0.65 | 1.4 | 0.04476 | 2.2102 × 10−5 |
Table 3.
Range of values for simulated process parameters.
Table 3.
Range of values for simulated process parameters.
Pouring Temperature (°C) | Pouring Time (s) | Shell Temperature (°C) | Shell Thickness (mm) | Heat Transfer Coefficient (J/m2·s·°C) |
---|
1680–1800 | 4–7 | 230–290 | 10 | 3347.2 |
Table 4.
L16(43) orthogonal table design.
Table 4.
L16(43) orthogonal table design.
No. | Pouring Temperature (°C) | Shell Temperature (°C) | Pouring Time (s) | No. | Pouring Temperature (°C) | Shell Temperature (°C) | Pouring Time (s) |
---|
1 | 1680 (1) | 230 (1) | 4 (1) | 9 | 1760 (3) | 230 (1) | 6 (3) |
2 | 1680 (1) | 250 (2) | 5 (2) | 10 | 1760 (3) | 250 (2) | 7 (4) |
3 | 1680 (1) | 270 (3) | 6 (3) | 11 | 1760 (3) | 270 (3) | 4 (1) |
4 | 1680 (1) | 290 (4) | 7 (4) | 12 | 1760 (3) | 290 (4) | 5 (2) |
5 | 1720 (2) | 230 (1) | 5 (2) | 13 | 1800 (4) | 230 (1) | 7 (4) |
6 | 1720 (2) | 250 (2) | 4 (1) | 14 | 1800 (4) | 250 (2) | 6 (3) |
7 | 1720 (2) | 270 (3) | 7 (4) | 15 | 1800 (4) | 270 (3) | 5 (2) |
8 | 1720 (2) | 290 (4) | 6 (3) | 16 | 1800 (4) | 290 (4) | 4 (1) |
Table 5.
Evaluation for regression modeling of shrinkage cavity and loosening number and volume.
Table 5.
Evaluation for regression modeling of shrinkage cavity and loosening number and volume.
Coefficient of Determination | Shrinkage Cavity Number | Shrinkage Cavity Volume | Shrinkage Loose Number | Shrinkage Loose Volume |
---|
R2 | 0.827 | 0.995 | 0.471 | 0.941 |
Adj.R2 | 0.808 | 0.994 | 0.411 | 0.934 |
Table 6.
Evaluation for neural network model of casing shrinkage number and volume.
Table 6.
Evaluation for neural network model of casing shrinkage number and volume.
Evaluation | Shrinkage Cavity Number | Shrinkage Cavity Volume | Shrinkage Loose Number | Shrinkage Loose Volume |
---|
Training R2 | 0.936 | 0.999 | 0.716 | 0.961 |
Validation R2 | 0.920 | 0.999 | 0.739 | 0.955 |
MSE | 6.281 | 0.10 | 6.26 | 0.766 |
Table 7.
Single-factor process parameter control variables.
Table 7.
Single-factor process parameter control variables.
Pouring Temperature (°C) | Shell Temperature (°C) | Pouring Time (s) |
---|
1680–1800 | 260 | 4 |
1740 | 230–290 | 4 |
1740 | 260 | 4–7 |
Table 8.
Range of variation in shrinkage cavity and loose defects in one-factor prediction experiments.
Table 8.
Range of variation in shrinkage cavity and loose defects in one-factor prediction experiments.
Factors | Range | Cavity Number | Cavity Volume (cc) | Loosening Number | Loosening Volume (cc) |
---|
Pouring temperature (°C) | 1680–1800 | 109–147 | 4.5–10.5 | 97–123 | 6–9.4 |
Shell temperature (°C) | 230–290 | 119–134 | 6.8–6.9 | 93–105 | 6.6–7.8 |
Pouring time (°C) | 4–7 | 122–156 | 4.5–8.8 | 96–107 | 4.4–7.5 |
Table 9.
Optimization window for key process parameters.
Table 9.
Optimization window for key process parameters.
Parameters | Original Range | Optimization Range |
---|
Pouring temperature (°C) | 1680–1800 | 1680–1700 |
Shell temperature (°C) | 230–290 | 270–290 |
Pouring time (s) | 4–7 | 5.8–7 |
Table 10.
Actual vs. predicted process parameter ranges.
Table 10.
Actual vs. predicted process parameter ranges.
Actual and Predicted Range | Parameters | Parameter Ranges |
---|
Actual | Smelting current (kA), smelting time (min), smelting metal (kg) | 41–42, 14–19, 381–425 |
Shell temperature (°C) | 271–340 |
Pouring time (s) | 5.7–6.8 |
Optimization window | Pouring temperature (°C) | 1680–1700 |
Shell temperature (°C) | 270–290 |
Pouring time (s) | 5.8–7 |