# Multi-Objective Optimization of Microstructure of Gravure Cell Based on Response Surface Method

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Response Surface Method (RSM)

#### 2.2. Multi-Objective Genetic Algorithm (MOGA)

## 3. Finite Element Analysis (FEA)

#### 3.1. Regular Hexagonal Cell Microstructure

#### 3.2. Modeling

_{1}) is the thickest, the two side walls (Z

_{2}) are the thinnest, and the bottom layer (Z

_{3}) is thicker. The size relationship between the three is roughly

_{1}is the cell size of the copper layer after engraving; and A

_{2}is the cell size after chrome plating.

^{-3}, elastic modulus was 250 Gpa, and Poisson’s ratio was 0.12. The density of the external copper layer was 8940 kg/m

^{-3}, elastic modulus was 117 Gpa, and Poisson’s ratio was 0.35. The initial parameters of the model are shown in Table 1. Free meshing was used, and 1,462,424 nodes and 958,026 elements were generated, as shown in Figure 4.

#### 3.3. Static Analysis

_{1}is the printing pressure, and F

_{2}is the scraping blade pressure.

^{8}$\mathsf{\mu}{\mathrm{m}}^{3}$. From the perspective of mechanics and solid printing production technology, the three values all have a certain optimization space.

## 4. Results and Discussions

#### 4.1. Design of Experiment (DOE)

_{1}), the base cell size (A), the screen wall width (C), and the cell depth (D) were used as design variables. The variation range of each variable depended on the common solid printing process. The thickness of the external copper layer was 100~150 $\mathsf{\mu}\mathrm{m}$, the thickness of the surface chrome layer was 6~12 $\mathsf{\mu}\mathrm{m}$, the number of screen line was 170~210 lpi, and the dot area percentage was between 80% and 90%. The design and combination of the experimental points was carried out by the CCD method, as shown in Table 2.

#### 4.2. Response Surface Analysis

#### 4.2.1. Full Second-Order Polynomials Response Surface Model

#### 4.2.2. Sensitivity Analysis of Optimized Parameters

_{1}), the base cell size (A), the screen wall width (C), and the cell depth (D) to the maximum deformation (DMAX), the maximum Von Mises stress (SMAX), and total volume (VTOT), which are shown in Figure 8.

#### 4.3. Pareto Optimal in Multi-objective Optimization

_{1}is 8.949 $\mathsf{\mu}\mathrm{m}$, A is 120.15 $\mathsf{\mu}\mathrm{m}$, C is 6.53 $\mathsf{\mu}\mathrm{m}$, D is 29.948 $\mathsf{\mu}\mathrm{m}$, it is the design optimization solution.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Grau, G.; Cen, J.; Kang, H.; Kitsomboonloha, R.; Scheideler, W.J.; Subramanian, V. Gravure-printed electronics: Recent progress in tooling development, understanding of printing physics, and realization of printed devices. Flex. Print. Electron.
**2016**, 1, 23. [Google Scholar] [CrossRef] - Deng, P.J.; Fang, W.; Lu, J.D. Study about Influencing of printing process on gravure printing ink transfer. In Research on Food Packaging Technology; Yun, O., Min, X., Li, Y.T., Xunting, L., Eds.; Trans Tech Publications Ltd.: Stafa-Zurich, Switzerland, 2014; Volume 469, pp. 301–304. [Google Scholar]
- Dong, W. Research of Gravure Plate-Making Engraving Directly By Laser; South China University of Technology: Guangzhou, China, 2013. [Google Scholar]
- Chen, W.; Lai, W.; Wang, Y.; Wang, K.; Lin, S.; Yen, Y.; Hong, H.; Chou, T. Ultrafast laser engraving method to fabricate gravure plate for printed metal-mesh touch panel. Micromachines
**2015**, 6, 1483–1489. [Google Scholar] [CrossRef][Green Version] - Hennig, G.; Selbmann, K.H.; Brockelt, A. Laser Engraving in Gravure Industry. In Workshop on Laser Applications in Europe; Gries, W., Pearsall, T.P., Eds.; SPIE: Bellingham, WA, USA, 2006; Volume 6157. [Google Scholar]
- Yin, X.; Kumar, S. Flow visualization of the liquid-emptying process in scaled-up gravure grooves and cells. Chem. Eng. Sci.
**2006**, 61, 1146–1156. [Google Scholar] [CrossRef] - Henniga, G.; Selbmann, K.H.; Pfinninger, S.; Brendel, J.; Bruning, S. Large scale laser microstructuring of gravure print rollers. In Photon Processing in Microelectronics and Photonics Vii; Holmes, A.S., Meunier, M., Arnold, C.B., Niino, H., Geohegan, D.B., Trager, F., Dubowski, J.J., Eds.; Spie-Int Soc Optical Engineering: Bellingham, WA, USA, 2008; Volume 6879. [Google Scholar]
- Hennig, G.; Resing, M.; Mattheus, S.; Neuenschwander, B.; Bruening, S. Laser Microstructuring and Processing in Printing Industry. In 2011 Conference on Lasers and Electro-Optics; IEEE: New York, NY, USA, 2011. [Google Scholar]
- Li, Z.L.; Xia, Q.X.; Qin, X.F.; Wang, S.Z. Research on Laser Gravure Image Loss Less Compression; IEEE Computer Soc.: Los Alamitos, CA, USA, 2009; p. 72. [Google Scholar]
- Deng, P.; Zhang, G.; Fang, W.; Guo, J. Research on Computing Model of the Cell Volume for Electronic Engraved Gravure. In Advances in Printing and Packaging Technologies; Yun, O.Y., Min, X., Li, Y., Liu, X.T., Eds.; Scientific.Net: Bäch SZ, Sitzerland, 2013; Volume 262, p. 355. [Google Scholar]
- Deng, P.; Zhang, G.; Wang, Y.; Fang, W. Influence of Screen Ruling and Engraving Needle Tip Angle on Ink Transfer for Gravure. In Printing and Packaging Study; Yun, O.Y., Min, X., Li, Y., Eds.; Scientific.Net: Bäch SZ, Sitzerland, 2011; Volume 174, pp. 215–218. [Google Scholar]
- Tian, J.; Zhang, C.; Wang, Q. Analysis of craniocerebral injury in facial collision accidents. PLoS ONE
**2020**, 15, e0240359. [Google Scholar] [CrossRef] - Tian, J.; Chen, Y.; Ma, Z. Numerical Simulation of Performance of an Air-Water Separator with Corrugated Plates for Marine Diesel Engines. Processes
**2020**, 8, 1617. [Google Scholar] [CrossRef] - Sundararaghavan, V.; Zabaras, N. Classification and reconstruction of three-dimensional microstructures using support vector machines. Comput. Mater. Sci.
**2005**, 32, 223–239. [Google Scholar] [CrossRef] - Fullwood, D.T.; Niezgoda, S.R.; Adams, B.L.; Kalidindi, S.R. Microstructure sensitive design for performance optimization. Prog. Mater. Sci.
**2010**, 55, 477–562. [Google Scholar] [CrossRef] - Guan, J.; Wang, G.C.; Guo, T.; Song, L.B.; Zhao, G.Q. The microstructure optimization of H-shape forgings based on preforming die design. Mater. Sci. Eng. A Struct. Mater. Prop. Microstruct. Process.
**2009**, 499, 304–308. [Google Scholar] [CrossRef] - Shabani, M.O.; Mazahery, A. The GA optimization performance in the microstructure and mechanical properties of MMNCs. Trans. Indian Inst. Metals
**2012**, 65, 77–83. [Google Scholar] [CrossRef] - Yin, Y.; Qi, R.; Zhang, H.; Xi, S.; Zhu, Y.; Liu, Z. Microstructure design to improve the efficiency of thermal barrier coatings. Theor. Appl. Mech. Lett.
**2018**, 8, 18–23. [Google Scholar] [CrossRef] - Noruzi, R.; Ghadai, S.; Bingol, O.R.; Krishnamurthy, A.; Ganapathysubramanian, B. NURBS-based microstructure design for organic photovoltaics. Comput. Aided Des.
**2020**, 118, 13. [Google Scholar] [CrossRef] - Hambli, R. Application of response surface method for FEM bending analysis. Int. J. Veh. Des.
**2005**, 39, 1–13. [Google Scholar] [CrossRef] - Brooghani, S.Y.A.; Khalili, K.; Shahri, S.E.E.; Kang, B.S. Loading path optimization of a hydroformed part using multilevel response surface method. Int. J. Adv. Manuf. Technol.
**2014**, 70, 1523–1531. [Google Scholar] [CrossRef] - Subasi, A.; Sahin, B.; Kaymaz, I. Multi-objective optimization of a honeycomb heat sink using Response Surface Method. Int. J. Heat Mass Transf.
**2016**, 101, 295–302. [Google Scholar] [CrossRef] - Liu, S. Multi-objective optimization design method for the machine tool’s structural parts based on computer-aided engineering. Int. J. Adv. Manuf. Technol.
**2015**, 78, 1053–1065. [Google Scholar] [CrossRef] - Zhou, G.; Ma, Z.D.; Cheng, A.G.; Li, G.Y.; Huang, J. Design optimization of a runflat structure based on multi-objective genetic algorithm. Struct. Multidiscip. Optim.
**2015**, 51, 1363–1371. [Google Scholar] [CrossRef] - Wen, T.; Xu, F.; Lu, T.J. Structural optimization of two-dimensional cellular metals cooled by forced convection. Int. J. Heat Mass Transf.
**2007**, 50, 2590–2604. [Google Scholar] [CrossRef] - Liu, G.; Hou, D.H.; Zhao, X.J.; Yuan, D.W.; Li, L.; Sun, Y.L. Power transformer’s electrostatic ring optimization based on ANSYS parametric design language and response surface methodology. Appl. Sci.
**2019**, 9, 4286. [Google Scholar] [CrossRef][Green Version] - Raeisian, L.; Niazmand, H.; Ebrahimnia-Bajestan, E.; Werle, P. Thermal management of a distribution transformer: An optimization study of the cooling system using CFD and response surface methodology. Int. J. Electr. Power Energy Syst.
**2019**, 104, 443–455. [Google Scholar] [CrossRef] - Li, J.I.; Liu, Z.J.; Jabbar, M.A.; Gao, X.K. Design optimization for cogging torque minimizatior using response surface methodology. IEEE Trans. Magn.
**2004**, 40, 1176–1179. [Google Scholar] [CrossRef] - Kazakov, P.V. The genetic algorithms for multi-objective optimization: Review. Inf. Tekhnologii
**2011**, 10, 2–8. [Google Scholar] - Liu, G.; Luo, R.; Liu, S. A new interval multi-objective optimization method for uncertain problems with dependent interval variables. Int. J. Comput. Methods
**2020**, 17. [Google Scholar] [CrossRef] - Fleming, C.F.P. Genetic algorithms for multiobjective optimization: Formulation discussion and generalization. Proceedings of The 5th International Conference on Genetic Algorithms; Morgan Kaufmann Publishers Inc.: San Francisco, CA, USA, 1993; pp. 416–423. [Google Scholar]
- Zhu, Z.; Cai, Y.-F.; Chen, L.; Xia, C.-G.; Destech Publicat, I.N.C. Research on the Parameters Optimization of Hydro-Mechanical Compound Transmission with Moga. In Proceedings of the 2018 International Conference on Electrical, Control, Automation and Robotics, Munich, Germany, 20–24 August 2018; Volume 307, pp. 47–54. [Google Scholar]
- Barbarosie, C.; Toader, A.-M. Shape and topology optimization for periodic problems. Struct. Multidiscip. Optim.
**2010**, 40, 381–391. [Google Scholar] [CrossRef] - Barbarosie, C.; Toader, A.M. Optimization of bodies with locally periodic microstructure by varying the periodicity pattern. Netw. Heterog. Media
**2014**, 9, 433–451. [Google Scholar] [CrossRef][Green Version] - Li, H.; Li, H.; Xiao, M.; Zhang, Y.; Fu, J.J.; Gao, L. Robust topology optimization of thermoelastic metamaterials considering hybrid uncertainties of material property. Compos. Struct.
**2020**, 248, 16. [Google Scholar] [CrossRef] - Li, N. Researcher on the Printing Pressure of the Gravure Printer; Xi’an University of Technology: Xi’an, China, 2009. [Google Scholar]
- Kuninaka, H.; Hayakawa, H. Contact and quasi-static impact of Hamilton system. J. Phys. Soc. Jpn.
**2006**, 75. [Google Scholar] [CrossRef][Green Version] - Sohn, D.; Won, H.-S.; Jang, B.; Kim, J.-H.; Lee, H.-J.; Choi, S.T. Extended JKR theory on adhesive contact between elastic coatings on rigid cylinders under plane strain. Int. J. Solids Struct.
**2015**, 71, 244–254. [Google Scholar] [CrossRef] - Lu, J.; Zhang, G.; Li, L. Research on Friction between Gravure Roller and Scraping Blade. In Research on Food Packaging Technology; Yun, O., Min, X., Li, Y.T., Xunting, L., Eds.; Scientific.Net: Bäch SZ, Sitzerland, 2014; Volume 469, pp. 399–403. [Google Scholar]
- Draper, N.R.S. Applied Regression Analysis; Wiley-Interscience: New York, NY, USA, 1998. [Google Scholar]
- Hsiao, J.C.; Shivam, K.; Chou, C.L.; Kam, T.Y. Shape design optimization of a robot arm using a surrogate-based evolutionary approach. Appl. Sci.
**2020**, 10, 2223. [Google Scholar] [CrossRef][Green Version]

**Figure 5.**(

**a**) Working schematic diagram of the printing plate. (

**b**) Contact force analysis of the printing plate cylinder.

**Figure 6.**(

**a**) Deformation nephogram of the cell structure. (

**b**) Von Mises stress nephogram of the cell structure.

**Figure 9.**Surface response diagram between three variables: (

**a**) Z

_{1}, C, and DMAX. (

**b**) Z

_{1}, C, and SMAX. (

**c**) T, A, and VTOT.

Name | Size | Name | Size |
---|---|---|---|

External copper layer thickness (T) | 120 μm | Base cell size (A) | 150 μm |

Surface chrome layer thickness (Z_{1}) | 8 μm | Screen wall width (C) | 10 μm |

Number of cells | 8 × 8 | Cell depth (D) | 30 μm |

Node | T $/\mathsf{\mu}{m}$ | Z_{1}$/\mathsf{\mu}{m}$ | $\mathbf{A}/\mathsf{\mu}{m}$ | C $/\mathsf{\mu}{m}$ | D $/\mathsf{\mu}{m}$ | DMAX $/\mathsf{\mu}{m}$ | SMAX $/{M}{p}{a}$ | $\mathbf{VTOT}/\mathsf{\mu}{{m}}^{3}$ |
---|---|---|---|---|---|---|---|---|

1 | 100 | 9 | 145 | 11.5 | 35.5 | 0.294 | 2.788 | 1.01 × 10^{8} |

2 | 117.916 | 8.149 | 137.916 | 9.942 | 42.442 | 0.276 | 2.461 | 1.07 × 10^{8} |

3 | 117.916 | 8.149 | 137.916 | 13.058 | 28.558 | 0.424 | 4.008 | 1.07 × 10^{8} |

4 | 117.916 | 8.149 | 152.083 | 9.942 | 28.558 | 0.27 | 2.639 | 1.3 × 10^{8} |

5 | 117.916 | 8.149 | 152.083 | 13.058 | 42.442 | 0.413 | 4.058 | 1.3 × 10^{8} |

6 | 117.916 | 9.85 | 137.916 | 9.942 | 28.558 | 0.250 | 1.71 | 1.07 × 10^{8} |

7 | 117.916 | 9.85 | 137.916 | 13.058 | 42.442 | 0.359 | 3.372 | 1.08 × 10^{8} |

8 | 117.916 | 9.85 | 152.083 | 9.942 | 42.442 | 0.244 | 1.802 | 1.3 × 10^{8} |

9 | 117.916 | 9.85 | 152.083 | 13.058 | 28.558 | 0.355 | 3.098 | 1.31 × 10^{8} |

10 | 125 | 6 | 145 | 11.5 | 35.5 | 0.474 | 5.315 | 1.25 × 10^{8} |

11 | 125 | 9 | 120 | 11.5 | 35.5 | 0.333 | 2.552 | 0.86 × 10^{8} |

12 | 125 | 9 | 145 | 6 | 35.5 | 0.164 | 1.392 | 1.24 × 10^{8} |

13 | 125 | 9 | 145 | 11.5 | 11 | 0.318 | 2.849 | 1.25 × 10^{8} |

14 | 125 | 9 | 145 | 11.5 | 35.5 | 0.318 | 2.902 | 1.25 × 10^{8} |

15 | 125 | 9 | 145 | 11.5 | 60 | 0.319 | 2.671 | 1.25 × 10^{8} |

16 | 125 | 9 | 145 | 17 | 35.5 | 0.635 | 5.507 | 1.27 × 10^{8} |

17 | 125 | 9 | 170 | 11.5 | 35.5 | 0.314 | 2.900 | 1.72 × 10^{8} |

18 | 125 | 12 | 145 | 11.5 | 35.5 | 0.278 | 1.720 | 1.26 × 10^{8} |

19 | 132.083 | 8.1499 | 137.916 | 9.942 | 28.558 | 0.29 | 2.391 | 1.19 × 10^{8} |

20 | 132.083 | 8.1499 | 137.916 | 13.058 | 42.442 | 0.44 | 3.76 | 1.2 × 10^{8} |

21 | 132.083 | 8.1499 | 152.083 | 9.942 | 42.442 | 0.283 | 2.688 | 1.45 × 10^{8} |

22 | 132.083 | 8.1499 | 152.083 | 13.058 | 28.558 | 0.427 | 4.053 | 1.46 × 10^{8} |

23 | 132.083 | 9.85 | 137.916 | 9.942 | 42.442 | 0.263 | 1.753 | 1.2 × 10^{8} |

24 | 132.083 | 9.85 | 137.916 | 13.058 | 28.558 | 0.375 | 3.478 | 1.2 × 10^{8} |

25 | 132.083 | 9.85 | 152.083 | 9.942 | 28.558 | 0.255 | 1.733 | 1.45 × 10^{8} |

26 | 132.083 | 9.85 | 152.083 | 13.058 | 42.442 | 0.369 | 3.107 | 1.46 × 10^{8} |

27 | 150 | 9 | 145 | 11.5 | 35.5 | 0.342 | 3.133 | 1.5 × 10^{8} |

Node | T $/\mathsf{\mu}{m}$ | Z_{1}$/\mathsf{\mu}{m}$ | $\mathbf{A}/\mathsf{\mu}{m}$ | C $/\mathsf{\mu}{m}$ | D $/\mathsf{\mu}{m}$ | DMAX $/\mathsf{\mu}{m}$ | SMAX $/{M}{p}{a}$ | $\mathbf{VTOT}/\mathsf{\mu}{{m}}^{3}$ |
---|---|---|---|---|---|---|---|---|

1 | 100.76 | 8.949 | 120.15 | 6.53 | 29.95 | 0.155 | 0.094 | 6.878 × 10^{7} |

2 | 100.52 | 9.042 | 120.24 | 6.269 | 55.04 | 0.158 | 1.4886 | 6.882 × 10^{7} |

3 | 100.3 | 8.5 | 120.96 | 6.349 | 38.68 | 0.157 | 0.220 | 6.943 × 10^{7} |

Node | T $/\mathsf{\mu}{m}$ | Z_{1}$/\mathsf{\mu}{m}$ | $\mathbf{A}/\mathsf{\mu}{m}$ | C $/\mathsf{\mu}{m}$ | D $/\mathsf{\mu}{m}$ | DMAX $/\mathsf{\mu}{m}$ | SMAX $/{M}{p}{a}$ | $\mathbf{VTOT}/\mathsf{\mu}{{m}}^{3}$ |
---|---|---|---|---|---|---|---|---|

Before | 120 | 8 | 150 | 10 | 30 | 0.27 | 2.739 | 1.284 × 10^{8} |

After | 100.76 | 8.949 | 120.15 | 6.53 | 29.95 | 0.155 | 0.094 | 6.879 × 10^{7} |

Change | The maximum deformation was reduced by 44.4%, and the total model volume was reduced by 46.3%. |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wu, S.; Xing, J.; Dong, L.; Zhu, H.
Multi-Objective Optimization of Microstructure of Gravure Cell Based on Response Surface Method. *Processes* **2021**, *9*, 403.
https://doi.org/10.3390/pr9020403

**AMA Style**

Wu S, Xing J, Dong L, Zhu H.
Multi-Objective Optimization of Microstructure of Gravure Cell Based on Response Surface Method. *Processes*. 2021; 9(2):403.
https://doi.org/10.3390/pr9020403

**Chicago/Turabian Style**

Wu, Shuang, Jiefang Xing, Ling Dong, and Honjuan Zhu.
2021. "Multi-Objective Optimization of Microstructure of Gravure Cell Based on Response Surface Method" *Processes* 9, no. 2: 403.
https://doi.org/10.3390/pr9020403