Simulation plan

A plan can be designed to get a simulation goal. The simulation plan consists of different issues such as parameters, nodes, models and others which are investigated in the simulation results to get the goal.

The simulation results are useful to study effective parameters during the printing process. So, one possibility to simulate the indirect gravure printing process will be investigated in this chapter.

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Figure 6-2 shows some cells and points on the pad surface which are called elements and nodes in the simulation results. They are produced after the meshing of the pad in the simulation process. Each point on the pad surface has a displacement in a 3D coordinate system during applying pressure on the substrate. The displacement can be described in XYZ Cartesian coordinate system.

The pad moves in Z-direction. A displacement in X-direction and Y-direction is occurred when the pad surface points have a contact with the substrate.

In the printing process, the pad surface transfers a 2D image on XY-plane of the substrate surface. So, a displacement of the pad surface points in X and Y directions affects on printing results distortion. The positions of pad surface points in X and Y directions before having a contact with the substrate are called initial positions or original positions in X and Y directions. During a pressing of the pad on the substrate, the surface points of the pad have a movement in comparison with their original position which is called pad displacement in X and Y directions.

So, as a case study a displacement of the pad surface during the printing process will be studied. A pad displacement depends on a force of the pad to the substrate which is called printing force. In this case study, the printing force for pad displacement is considered 100 N, because this is a typical value supported by four different pads of Figure 6-3 with four different hardnesses.

(a) (b)

Figure 6-2: The pad surface points for an undeformed pad (a) and the deformed pad under pressing (b) are shown. An arc between the pad tip and pad side is displayed here. Some points on

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this path were numbered from 0 to 8 as an example. These points are some nodes in the simulation process with FEM software ABAQUS.

Further, the pad surface has a circular symmetric shape around Z-axis. The pad tip is located in the center of Z-axis. So, the displacement of the pad surface points located on a circle with the same radius from Z-axis (as a center of this circle), are similar to each other. So, the displacement behavior of the pad surface points located on an arc between the pad tip and a pad edge, can be a suitable sample to investigate the points displacement on the pad surface. Therefore, in this study, the displacement of points located on this arc will be investigated as a representative of the pad surface points.

Figure 6-2 shows eight points which are located on an arc between the pad tip and the pad edge as an example. The displacement of the pad surface in this area will be discussed in the simulation results of this chapter.

In addition, the pad displacement depends on the pad geometry and pad hardnesses. So, to evaluate this issue, four different pads and four different hardnesses are investigated.

The pads with different geometries are called pad 1, pad 2, pad 3 and pad 4 which were shown in Figure 5-7 and their designing method was described in chapter 5.2. The equations in chapter 5.1 describe the designing parameters of a pad. In this case study, an effect of the pad height on the pad surface displacement is investigated. So, the pad height is considered as a variable and other designing parameters are considered constant. Figure 6-3 shows four different pads and related heights in a comparative view. According to Figure 6-3, changing of the pad height leads to pad sharpness changes. In this figure, the tip of the pad with H4 is sharper than other pads with smaller heights. For pads with different geometries, it is expected that points on the pad surface indicate different displacements during pressing.

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Figure 6-3: The comparative view of four different pads. H1, H2, H3 and H4 are the heights of pad 1, pad 2, pad 3 and pad 4 with amounts of 44.5, 52.5, 60.2 and 68.1 mm, respectively. Other parameters and single view of these pads were described in chapter 5.2.

The pad gets the ink from printing form cells and then transfers the ink to the substrate.

The printed image in the indirect gravure printing method is made of small printed dots positioned together. The displacement of the pad surface in X and Y direction will affect displacement and deformation of printed dots’ frame which can lead to a decrease in the printing results quality. In addition, the printed dots on a circle with the same radius from the center of the pad (pad tip) show the same displacement because of circular symmetry of the pad surface.

Therefore, X and Y Cartesian coordinate system is converted to Polar coordinate system. In a Polar coordinate system, the results are presented with a radius (R) which is a distance from a reference point and an angle (Theta) which is an angle from the reference direction. Here, the reference point is the pad tip, which is the contact point of X and Y axes. The reference direction is X-axis direction. So, in simulation results of this chapter, the results are presented with polar variables of R and Theta. R is a distance from the pad tip with the unit of millimeter (mm) and Theta is an angle from X-axis with the unit of degree which is shown with deg or °. Figure 6-4 shows schematically a concept of R and Theta variables.

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Figure 6-4: The schematic of pad surface points in a Polar coordinate system. The green and red points are located on circles with a radius of R1 and R2 from the pad center, respectively. Theta is an angle of each point from X-axis. The white point in the center is the pad center. The points with

“X” markers which are located in the downward direction of the pad center, are a projection of pad surface points onto XY-plane.

In Figure 6-4, some points are marked in two circular positions on the pad surface with red and green colors. Their projections are displayed on the substrate surface with “X”

markers and with the same color of the points on the pad surface. The distance between the projection of points and pad center is displayed with R.