Modeling the Producibility of 3D Printing in Polylactic Acid Using Artificial Neural Networks and Fused Filament Fabrication
Abstract
:1. Introduction
2. Materials and Methods
2.1. Response Surface Methodology and Artificial Neural NetworkGenetic Algorithm (ANNGA)
2.2. Experimental Work
3. Results
3.1. Toughness
3.2. Part Thickness
3.3. Production Cost
3.4. ANN and ANNGA Techniques
3.5. Numerical Optimization
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Factor  Unit  Levels  

−2  −1  0  1  2  
LT  mm  0.1  0.15  0.2  0.25  0.3 
IP  %  10  20  30  40  50 
ET  C  190  200  210  220  230 
Run  Input Factors  Output Responses  Type of Fracture  

LT  IP  ET  Toughness (Nmm)  Part Thickness (mm)  Production Cost ($)  
1  0.20  30.00  210.00  1829.27  3.98  17.73  Brittle 
2  0.20  30.00  210.00  1394.35  3.84  17.73  Brittle 
3  0.15  40.00  220.00  1157.86  3.88  21.72  Brittle 
4  0.30  30.00  210.00  5164.36  3.68  13.77  Tough 
5  0.20  30.00  210.00  1674.03  4.02  17.73  Brittle 
6  0.25  40.00  200.00  5144.17  4.00  15.76  Tough 
7  0.25  20.00  200.00  1835.62  3.82  15.25  Brittle 
8  0.15  20.00  220.00  2239.94  4.48  20.2  Brittle 
9  0.20  30.00  210.00  4112.96  4.04  17.73  Tough 
10  0.15  40.00  200.00  1520.79  3.98  21.72  Brittle 
11  0.20  30.00  210.00  1140.16  4.08  17.73  Brittle 
12  0.20  10.00  210.00  1167.21  3.86  16.72  Brittle 
13  0.10  30.00  210.00  830.976  3.98  27.19  Brittle 
14  0.15  20.00  200.00  817.052  4.08  20.2  Brittle 
15  0.20  30.00  230.00  2644.34  4.08  17.23  Brittle 
16  0.20  30.00  190.00  2075.45  3.74  17.23  Brittle 
17  0.20  50.00  210.00  2462.57  3.9  18.25  Brittle 
18  0.25  40.00  220.00  4489.05  4.12  15.76  Tough 
19  0.25  20.00  220.00  5046.5  3.8  15.25  Tough 
20  0.20  30.00  210.00  1393.06  3.86  17.73  Brittle 
Accuracy and Performance Index  Description 

Correlation coefficient = $\frac{N{{\displaystyle \sum}}_{}^{}{(AP)}^{}{{\displaystyle \sum}}_{}^{}{(A)}^{}{{\displaystyle \sum}}_{}^{}{(P)}^{}}{\sqrt{[N{{\displaystyle \sum}}_{}^{}{A}^{2}{({{\displaystyle \sum}}_{}^{}A)}^{}{}^{2}]{[N{{\displaystyle \sum}}_{}^{}{P}^{2}{({{\displaystyle \sum}}_{}^{}AP)}^{}{}^{2}]}^{}{}^{}}}$ 

RMSE =$\sqrt{\frac{1}{N}{\displaystyle \sum}_{}^{}{(AP)}^{2}}$ 
Property  Value 

Full name  Polylactic acid (PLA) 
Melting point  150 to 160 °C (302 to 320 °F) 
Glass transition  60–65 °C 
Injection mold temperature  178 to 240 °C (353 to 464 °F) 
Density  1.210–1.430 g·cm^{−3} 
Chemical formula  (C_{3}H_{4}O_{2})n 
Crystallinity  37% 
Tensile modulus  2.7–16 GPa 
molecular weight (Mw)  112 kg/mol ± 1733 
Polydispersity (M_{W}/M_{N})  1.65 ± 0.05 
No  Build Parameters  Unit  Value 

1  Nozzle diameter  mm  0.45 
2  Extrusion width  mm  0.45 
3  Top solid layer    6 
4  Bottom solid layers    6 
5  Default printing speed  mm/min  3600 
6  Retraction speed  mm/min  1800 
7  Outline overlap    Full honeycomb 
8  Interior fill percentage  %  15 
Source  Sum of Squares (SOS)  Df  Mean Square (MS)  FValue (Fv)  PValue (Pv) 

Model  1.694 × 10^{−3}  4  4.235 × 10^{−4}  13.04  <0.0001 
LT  1.228 × 10^{−3}  1  1.228 × 10^{−3}  37.81  <0.0001 
IP  1.250 × 10^{−4}  1  1.250 × 10^{−4}  3.85  0.0687 
ET  8.980 × 10^{−5}  1  8.980 × 10^{−5}  2.76  0.1171 
(IP) × (ET)  2.513 × 10^{−4}  1  2.513 × 10^{−4}  7.74  0.0140 
Residual  4.872 × 10^{−4}  15  3.248 × 10^{−5}  
Lack of Fit (LOF)  1.747 × 10^{−4}  10  1.747 × 10^{−5}  0.28  0.9591 
Pure Error (PR)  3.125 × 10^{−4}  5  6.250 × 10^{−5}  
Cor Total (CT)  2.181 × 10^{−3}  19  
Pred RSquare  0.6747  Adj RSquared  0.7171  RSquared  0.7766 
Source  SOS  Df  MS  Fv  Pv 

Model  0.89  6  0.15  4.46  0.0115 
LT  0.20  1  0.20  5.98  0.0294 
IP  0.024  1  0.024  0.73  0.4096 
E)  0.15  1  0.15  4.48  0.0542 
(LT) × (IP)  0.36  1  0.36  10.92  0.0057 
(LT) × (ET)  0.061  1  0.061  1.85  0.1968 
(IP) × (ET)  0.092  1  0.092  2.79  0.1185 
Residual  0.43  13  0.033  
PR  0.049  5  9720 × 10^{−3}  
LOF  0.38  8  0.048  4.91  0.0482 
CT  1.32  19  
Pred RSquare  −0.5694  Adj RSquared  0.5220  RSquared  0.6730 
Source  SOS  Df  MS  Fv  Pv 

Model  6.769 × 10^{−5}  5  1.354 × 10^{−5}  1464.91  <0.0001 
LT  6.592 × 10^{−5}  1  6.592 × 10^{−5}  7133.12  <0.0001 
IP  1.555 × 10^{−6}  1  1.555 × 10^{−6}  168.23  <0.0001 
ET  0.000  1  0.000  0.000  1.0000 
IP^{2}  4.940 × 10^{−8}  1  4.940 × 10^{−8}  5.35  0.0365 
ET^{2}  1.927 × 10^{−7}  1  1.927 × 10^{−7}  20.85  0.0004 
PE  0.000  5  0.000  
LOF  1.294 × 10^{−7}  9  1.438 × 10^{−8}  
Residual  1.294 × 10^{−7}  14  9.241 × 10^{−9}  
CT  6.782 × 10^{−5}  19  
Pred RSquare  0.9940  Adj RSquared  0.9974  RSquared  0.9981 
Output Factor  ANN  Correlation Coefficient  RMSE  ANNGA  Correlation Coefficient  RMSE  

No. of Neurons  Pop. Size  Max Gen.  
Toughness (Nmm)  10  0.7877  924.5529274  50  320  0.9439  633.6373621 
12  0.8782  908.0737946  100  210  0.8692  734.6853877  
14  0.7964  893.2048644  150  360  0.9642  453.8843405  
16  0.8789  694.1594251  200  110  0.9186  654.6824998  
Part thickness (mm)  10  0.7671  0.12949  50  320  0.9362  0.045035408 
12  0.8788  0.075333178  100  210  0.93  0.042059003  
14  0.5173  0.084915266  150  360  0.7768  0.059754932  
16  0.6324  0.099691882  200  110  0.8538  0.077821436  
Production cost ($)  10  0.8531  1.960663  50  320  09485  1.288136157 
12  0.9636  0.970732923  100  210  0.8956  1.556494043  
14  0.8235  3.830106928  150  360  0.9754  1.011613758  
16  0.842  2.267871729  200  110  0.9105  1.29979527 
Output Factor  ANN  Correlation Coefficient  RMSE  ANNGA  Correlation Coefficient  RMSE  

No. of Neurons  Pop. Size  Max Gen.  
Toughness (Nmm)  12  0.91  651.7539629  150  360  0.9791  277.4633823 
Part thickness (mm)  0.8911  0.118439425  0.9904  0.036062371  
Production Cost ($)  0.938  0.861473905  0.9762  0.569953845 
Responses/Parameters  Name  Goal  Lower Limit  Upper Limit  Lower Weight  Upper Weight  Importance  

Parameters  LT  Is in range  0.1  0.3  1  1    
IP  Is in range  10  50  1  1    
ET  Is in range  190  230  1  1    
Responses  Criteria  Toughness  Maximum  817  5500  1  1  1 
Thickness  is goal = 4  3.68  4.98  1  1  1  
Cost  Minimum  13.77  27.19  1  1  1 
Sol.  Optimum Inputs  Desirability  Output Responses  

LT  IP  ET  Toughness (Nmm)  Thickness (mm)  Production Cost ($)  
1  0.28  38  222  0.99  Actual  5097.727  3.72  14.77 
Predicted  5399.99  4.000  14.372  
Error%  −5.93%  −7.5%  2.23% 
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Meiabadi, M.S.; Moradi, M.; Karamimoghadam, M.; Ardabili, S.; Bodaghi, M.; Shokri, M.; Mosavi, A.H. Modeling the Producibility of 3D Printing in Polylactic Acid Using Artificial Neural Networks and Fused Filament Fabrication. Polymers 2021, 13, 3219. https://doi.org/10.3390/polym13193219
Meiabadi MS, Moradi M, Karamimoghadam M, Ardabili S, Bodaghi M, Shokri M, Mosavi AH. Modeling the Producibility of 3D Printing in Polylactic Acid Using Artificial Neural Networks and Fused Filament Fabrication. Polymers. 2021; 13(19):3219. https://doi.org/10.3390/polym13193219
Chicago/Turabian StyleMeiabadi, Mohammad Saleh, Mahmoud Moradi, Mojtaba Karamimoghadam, Sina Ardabili, Mahdi Bodaghi, Manouchehr Shokri, and Amir H. Mosavi. 2021. "Modeling the Producibility of 3D Printing in Polylactic Acid Using Artificial Neural Networks and Fused Filament Fabrication" Polymers 13, no. 19: 3219. https://doi.org/10.3390/polym13193219