In order to improve the structural stiffness of the gravure cell structure in the solid printing process and realize a lightweight design, a multi-objective optimization design method was proposed to optimize the parameters of the direct laser engraving of the cell structure. In this paper, based on the characteristics of the cell structure and the analysis of the contact force, the ANSYS parametric design language (APDL) was used to conduct a finite element analysis on the microstructure of the regular hexagonal cell. We found that there is a certain optimization space. Then, a response surface (RSM) method optimization model, using a central composite design (CCD), was established to obtain, and then analyze, the sensitivity of each design variable to the objective functions. Finally, a multi-objective genetic algorithm (MOGA) was used to solve the model. The optimization results show that the maximum deformation was reduced by 44.4%, and the total volume was reduced by 46.3%. By comparing with the model before optimization, the rationality and effectiveness of this method were verified. This shows that the method can be effectively applied to the design optimization of gravure cell microstructure, and it provides theoretical support for new cell design.

Based on the actual measurement of the shear-thickening properties of water-based inks, in order to improve the ink transfer rate, the PLIC (Piecewise Linear Interface Construction) interface tracking method and the VOF (Volume of Fluid) method are used to simulate the transfer process of the shear-thickening liquid between the U-shaped cell and the upwardly moving plate. The effects of substrate surface wettability, cell contact angle, and cell depth on liquid transfer were studied. The results showed that all can increase the liquid transfer rate, and the change of the cell contact angle also led to the difference in the breaking time of the liquid filament. In addition, the shallow plate effect was discovered in the study of cell depth. The shallow plate effect is a phenomenon by which the amount of liquid transferred and the liquid transfer rate are greatly improved when the depth of the cell decreases to a certain limit value. In addition, for the U-shaped cell, the optimization method combining the shallow printing plate effect and fillet can greatly improve the liquid transfer rate and solve the undesirable problems such as plate blocking. After optimization, a liquid transfer rate of about 85% can be achieved.

The roll-to-roll gravure printing ink transfer process plays an important role in enhancing printing quality and saving on costs. The static analysis and fluid–solid interaction method are used for the first time to conduct a systematic study on the coupling between the fluid flow state and the solid deformation in the whole process of roll-to-roll gravure printing. The static compression stage, the initial moment of ink transfer, and the process of ink passing through the gap between two rollers and the separation of the ink layer with the rotation of two rollers are considered. The effect of ink layer thickness on the ink transfer process is studied. At a printing pressure of 0.2 MPa and a printing velocity of 200 rpm, the ink thickness has a great influence on the ink flow state, which leads to backflow; the phenomenon causes irregularities in the effective ink transfer ratio. The critical ink layer thickness is 70 µm under the above gravure printing conditions. This should not be exceeded to ensure the stability of ink transfer. Under the above printing conditions, when the ink layer thickness is in the range of 30–50 µm, there is no ink backflow phenomenon and the width of the ink flow channel is relatively large, and the effective ink ratio is almost stable at 50%. This study is helpful for controlling the ink quantity in the gravure printing, providing strong theoretical support for the improvement of the gravure printing process, and promoting the application of the water-based ink.

Gravure printing is widely used in food, pharmaceutical, and other packaging industries. As a green printing material, water-based ink has problems such as non-volatile and poor drying on non-absorbent packaging substrates, which has a great impact on its application. To solve these difficulties, this study adopts the volume of fluid (VOF) method and user-defined function (UDF) to establish a multiphase flow impinging air jets drying model of water-based ink in the gravure printing process, taking a water-based ink droplet as an example. The model was used to simulate the ink drying state in the impinging air jets region and analyze the effects of impinging air jets’ temperature and velocity, as well as ink viscosity and thickness, on the ink drying efficiency. Meanwhile, the heat and mass transfer mechanism between impinging air jets and water-based ink was investigated. The results show that the higher impinging air jet temperature and velocity, the faster the drying rate of the ink; a lower viscosity and thinner thickness of ink can also enhance the drying efficiency of the ink. The multiphase impinging air jets drying model based on the computational fluid dynamics (CFD) method provides a new research idea for the analysis of drying characteristics of water-based ink on non-absorbent substrates, and the research results provide theoretical support to promote its application.