Acta Metallurgica Sinica (English Letters) ›› 2014, Vol. 27 ›› Issue (6): 1012-1017.DOI: 10.1007/s40195-014-0115-6
• Orginal Article • Previous Articles Next Articles
He Huan, Yang Chunli, Chen Zhe, Lin Sanbao(), Fan Chenglei
Received:
2013-09-06
Revised:
2014-01-20
Online:
2014-08-07
Published:
2015-07-23
He Huan, Yang Chunli, Chen Zhe, Lin Sanbao, Fan Chenglei. Strength Prediction of Aluminum-Stainless Steel-Pulsed TIG Welding-Brazing Joints with RSM and ANN[J]. Acta Metallurgica Sinica (English Letters), 2014, 27(6): 1012-1017.
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Material | C | Mn | Mg | Si | Cu | Zn | Ti | Ni | Cr | Fe | Al |
---|---|---|---|---|---|---|---|---|---|---|---|
SUS321 | 0.12 | 2 | - | 1 | - | - | 0.2 | 8-10 | 17-19 | Bal. | - |
5A06 | - | 0.5-0.8 | 5.8-6.8 | 0.4 | 0.1 | 0.2 | 0.1 | - | - | 0.4 | Bal. |
ER1100 | - | 0.05 | - | x | 0.05-0.2 | 0.1 | - | - | - | 0.95-x | Bal. |
Table 1 Chemical compositions of base metal and filler metal (wt%)
Material | C | Mn | Mg | Si | Cu | Zn | Ti | Ni | Cr | Fe | Al |
---|---|---|---|---|---|---|---|---|---|---|---|
SUS321 | 0.12 | 2 | - | 1 | - | - | 0.2 | 8-10 | 17-19 | Bal. | - |
5A06 | - | 0.5-0.8 | 5.8-6.8 | 0.4 | 0.1 | 0.2 | 0.1 | - | - | 0.4 | Bal. |
ER1100 | - | 0.05 | - | x | 0.05-0.2 | 0.1 | - | - | - | 0.95-x | Bal. |
Peak current (A) | Pulse on time (%) | Basic current (A) | Frequency of pulsed current (Hz) |
---|---|---|---|
145-155 | 35-45 | 55-65 | 28-76 |
Table 2 Major parameters and corresponding working limits
Peak current (A) | Pulse on time (%) | Basic current (A) | Frequency of pulsed current (Hz) |
---|---|---|---|
145-155 | 35-45 | 55-65 | 28-76 |
Welding speed (mm/min) | Balance (%) | Frequency of AC (Hz) |
---|---|---|
180 | 50 | 100 |
Table 3 Fixed parameters
Welding speed (mm/min) | Balance (%) | Frequency of AC (Hz) |
---|---|---|
180 | 50 | 100 |
Number | Peak current (A) | Pulse on time (%) | Basic current (A) | Frequency of pulsed current (Hz) | Tensile strength (MPa) |
---|---|---|---|---|---|
No. 1 | 145.00 | 35.00 | 55.00 | 76.00 | 156.58 |
No. 2 | 150.00 | 40.00 | 60.00 | 52.00 | 198.30 |
No. 3 | 150.00 | 40.00 | 60.00 | 52.00 | 204.69 |
No. 4 | 145.00 | 35.00 | 55.00 | 28.00 | 163.68 |
No. 5 | 145.00 | 35.00 | 65.00 | 76.00 | 186.93 |
No. 6 | 155.00 | 45.00 | 55.00 | 76.00 | 211.06 |
No. 7 | 155.00 | 45.00 | 65.00 | 28.00 | 213.59 |
No. 8 | 145.00 | 35.00 | 65.00 | 28.00 | 197.86 |
No. 9 | 150.00 | 40.00 | 60.00 | 4.00 | 213.55 |
No. 10 | 145.00 | 45.00 | 55.00 | 76.00 | 195.54 |
No. 11 | 140.00 | 40.00 | 60.00 | 52.00 | 188.34 |
No. 12 | 150.00 | 30.00 | 60.00 | 52.00 | 194.90 |
No. 13 | 150.00 | 40.00 | 60.00 | 52.00 | 188.90 |
No. 14 | 150.00 | 40.00 | 60.00 | 52.00 | 207.69 |
No. 15 | 150.00 | 50.00 | 60.00 | 52.00 | 234.02 |
No. 16 | 160.00 | 40.00 | 60.00 | 52.00 | 203.15 |
No. 17 | 155.00 | 45.00 | 65.00 | 76.00 | 216.29 |
No. 18 | 150.00 | 40.00 | 50.00 | 52.00 | 187.26 |
No. 19 | 145.00 | 45.00 | 65.00 | 28.00 | 222.22 |
No. 20 | 155.00 | 45.00 | 55.00 | 28.00 | 202.53 |
No. 21 | 155.00 | 35.00 | 65.00 | 28.00 | 198.73 |
No. 22 | 150.00 | 40.00 | 70.00 | 52.00 | 212.64 |
No. 23 | 150.00 | 40.00 | 60.00 | 100.00 | 190.96 |
No. 24 | 155.00 | 35.00 | 55.00 | 76.00 | 188.69 |
No. 25 | 155.00 | 35.00 | 65.00 | 76.00 | 197.68 |
No. 26 | 145.00 | 45.00 | 55.00 | 28.00 | 209.70 |
No. 27 | 150.00 | 40.00 | 60.00 | 52.00 | 201.50 |
No. 28 | 145.00 | 45.00 | 65.00 | 76.00 | 210.24 |
No. 29 | 155.00 | 35.00 | 55.00 | 28.00 | 180.51 |
No. 30 | 150.00 | 40.00 | 60.00 | 52.00 | 206.19 |
No. 31 | 150.00 | 40.00 | 60.00 | 52.00 | 196.00 |
Table 4 Parameters and tensile strengths for samples of central composite design
Number | Peak current (A) | Pulse on time (%) | Basic current (A) | Frequency of pulsed current (Hz) | Tensile strength (MPa) |
---|---|---|---|---|---|
No. 1 | 145.00 | 35.00 | 55.00 | 76.00 | 156.58 |
No. 2 | 150.00 | 40.00 | 60.00 | 52.00 | 198.30 |
No. 3 | 150.00 | 40.00 | 60.00 | 52.00 | 204.69 |
No. 4 | 145.00 | 35.00 | 55.00 | 28.00 | 163.68 |
No. 5 | 145.00 | 35.00 | 65.00 | 76.00 | 186.93 |
No. 6 | 155.00 | 45.00 | 55.00 | 76.00 | 211.06 |
No. 7 | 155.00 | 45.00 | 65.00 | 28.00 | 213.59 |
No. 8 | 145.00 | 35.00 | 65.00 | 28.00 | 197.86 |
No. 9 | 150.00 | 40.00 | 60.00 | 4.00 | 213.55 |
No. 10 | 145.00 | 45.00 | 55.00 | 76.00 | 195.54 |
No. 11 | 140.00 | 40.00 | 60.00 | 52.00 | 188.34 |
No. 12 | 150.00 | 30.00 | 60.00 | 52.00 | 194.90 |
No. 13 | 150.00 | 40.00 | 60.00 | 52.00 | 188.90 |
No. 14 | 150.00 | 40.00 | 60.00 | 52.00 | 207.69 |
No. 15 | 150.00 | 50.00 | 60.00 | 52.00 | 234.02 |
No. 16 | 160.00 | 40.00 | 60.00 | 52.00 | 203.15 |
No. 17 | 155.00 | 45.00 | 65.00 | 76.00 | 216.29 |
No. 18 | 150.00 | 40.00 | 50.00 | 52.00 | 187.26 |
No. 19 | 145.00 | 45.00 | 65.00 | 28.00 | 222.22 |
No. 20 | 155.00 | 45.00 | 55.00 | 28.00 | 202.53 |
No. 21 | 155.00 | 35.00 | 65.00 | 28.00 | 198.73 |
No. 22 | 150.00 | 40.00 | 70.00 | 52.00 | 212.64 |
No. 23 | 150.00 | 40.00 | 60.00 | 100.00 | 190.96 |
No. 24 | 155.00 | 35.00 | 55.00 | 76.00 | 188.69 |
No. 25 | 155.00 | 35.00 | 65.00 | 76.00 | 197.68 |
No. 26 | 145.00 | 45.00 | 55.00 | 28.00 | 209.70 |
No. 27 | 150.00 | 40.00 | 60.00 | 52.00 | 201.50 |
No. 28 | 145.00 | 45.00 | 65.00 | 76.00 | 210.24 |
No. 29 | 155.00 | 35.00 | 55.00 | 28.00 | 180.51 |
No. 30 | 150.00 | 40.00 | 60.00 | 52.00 | 206.19 |
No. 31 | 150.00 | 40.00 | 60.00 | 52.00 | 196.00 |
Item | Sum of squares | Degree of freedom | Mean square | F | Probability |
---|---|---|---|---|---|
Model | 6,586.67 | 10 | 658.67 | 17.29 | <0.0001 |
I p | 383.60 | 1 | 383.60 | 10.07 | 0.0048 |
t p | 3,474.02 | 1 | 3,474.02 | 91.18 | <0.0001 |
I b | 1,441.66 | 1 | 1,441.66 | 37.84 | <0.0001 |
f | 209.98 | 1 | 209.98 | 5.51 | 0.0293 |
I p × t p | 187.62 | 1 | 187.62 | 4.92 | 0.0382 |
I p × I b | 145.50 | 1 | 145.50 | 3.82 | 0.0648 |
I p × f | 244.38 | 1 | 244.38 | 6.41 | 0.0198 |
I b × t p | 145.38 | 1 | 145.38 | 3.82 | 0.0649 |
I p 2 | 123.53 | 1 | 123.53 | 3.24 | 0.0869 |
t p 2 | 200.65 | 1 | 200.65 | 5.27 | 0.0327 |
Residual | 761.98 | 20 | 38.10 | - | - |
Lack of fit | 506.31 | 14 | 36.17 | 0.85 | 0.6282 |
Pure error | 255.67 | 6 | 42.61 | - | - |
Table 5 Analysis of variance
Item | Sum of squares | Degree of freedom | Mean square | F | Probability |
---|---|---|---|---|---|
Model | 6,586.67 | 10 | 658.67 | 17.29 | <0.0001 |
I p | 383.60 | 1 | 383.60 | 10.07 | 0.0048 |
t p | 3,474.02 | 1 | 3,474.02 | 91.18 | <0.0001 |
I b | 1,441.66 | 1 | 1,441.66 | 37.84 | <0.0001 |
f | 209.98 | 1 | 209.98 | 5.51 | 0.0293 |
I p × t p | 187.62 | 1 | 187.62 | 4.92 | 0.0382 |
I p × I b | 145.50 | 1 | 145.50 | 3.82 | 0.0648 |
I p × f | 244.38 | 1 | 244.38 | 6.41 | 0.0198 |
I b × t p | 145.38 | 1 | 145.38 | 3.82 | 0.0649 |
I p 2 | 123.53 | 1 | 123.53 | 3.24 | 0.0869 |
t p 2 | 200.65 | 1 | 200.65 | 5.27 | 0.0327 |
Residual | 761.98 | 20 | 38.10 | - | - |
Lack of fit | 506.31 | 14 | 36.17 | 0.85 | 0.6282 |
Pure error | 255.67 | 6 | 42.61 | - | - |
Number | Peak current (A) | Pulse on time (%) | Basic current (A) | Frequency (Hz) | Predicted tensile strength (MPa) | Experimental tensile strength (MPa) | Relative error (%) |
---|---|---|---|---|---|---|---|
No. 1 | 140 | 40 | 56 | 100 | 150.16 | 195.47 | 23.18 |
No. 2 | 140 | 40 | 65 | 25 | 208.63 | 211.20 | 1.22 |
No. 3 | 140 | 50 | 60 | 4 | 252.51 | 228.36 | 10.58 |
No. 4 | 160 | 50 | 54 | 100 | 234.44 | 198.35 | 18.20 |
No. 5 | 150 | 50 | 70 | 52 | 236.94 | 238.29 | 0.56 |
Table 6 Results of prediction by RSM and the relative errors
Number | Peak current (A) | Pulse on time (%) | Basic current (A) | Frequency (Hz) | Predicted tensile strength (MPa) | Experimental tensile strength (MPa) | Relative error (%) |
---|---|---|---|---|---|---|---|
No. 1 | 140 | 40 | 56 | 100 | 150.16 | 195.47 | 23.18 |
No. 2 | 140 | 40 | 65 | 25 | 208.63 | 211.20 | 1.22 |
No. 3 | 140 | 50 | 60 | 4 | 252.51 | 228.36 | 10.58 |
No. 4 | 160 | 50 | 54 | 100 | 234.44 | 198.35 | 18.20 |
No. 5 | 150 | 50 | 70 | 52 | 236.94 | 238.29 | 0.56 |
Parameters | Value |
---|---|
Number of input layer neurons | 4 |
Number of hidden layer neurons | 8 |
Number of output layer neurons | 1 |
Rate of learning | 0.4 |
Momentum factor | 0.5 |
Algorithm | BP with momentum term |
Table 7 Determined parameters of the networks
Parameters | Value |
---|---|
Number of input layer neurons | 4 |
Number of hidden layer neurons | 8 |
Number of output layer neurons | 1 |
Rate of learning | 0.4 |
Momentum factor | 0.5 |
Algorithm | BP with momentum term |
Number | Peak current (A) | Pulse on time (%) | Basic current (A) | Frequency (Hz) | Predicted value (MPa) | Experimental value (MPa) | Relative error (%) |
---|---|---|---|---|---|---|---|
No. 1 | 140 | 40 | 56 | 100 | 181.98 | 195.47 | 6.9 |
No. 2 | 140 | 40 | 65 | 25 | 213.16 | 211.20 | 0.9 |
No. 3 | 140 | 50 | 60 | 4 | 216.28 | 228.36 | 5.2 |
No. 4 | 160 | 50 | 54 | 100 | 209.79 | 198.35 | 5.5 |
No. 5 | 150 | 50 | 70 | 52 | 216.30 | 238.29 | 9.2 |
Table 8 Results of prediction by ANN and relative errors
Number | Peak current (A) | Pulse on time (%) | Basic current (A) | Frequency (Hz) | Predicted value (MPa) | Experimental value (MPa) | Relative error (%) |
---|---|---|---|---|---|---|---|
No. 1 | 140 | 40 | 56 | 100 | 181.98 | 195.47 | 6.9 |
No. 2 | 140 | 40 | 65 | 25 | 213.16 | 211.20 | 0.9 |
No. 3 | 140 | 50 | 60 | 4 | 216.28 | 228.36 | 5.2 |
No. 4 | 160 | 50 | 54 | 100 | 209.79 | 198.35 | 5.5 |
No. 5 | 150 | 50 | 70 | 52 | 216.30 | 238.29 | 9.2 |
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