Simulation validation

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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.

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hardness to consider the possibility of measurement error because of the pad material or the pad production process. For example, nine tests with same procedure is performed for a pad with model pad 2 and hardness of 3 Shore A. Then, an average and a deviation between these nine test results (experiments) are calculated. Figure 6-5 shows average, minimum and maximum curves of nine tests (experiments) which were performed in the same procedure on a pad with model of pad 2 and hardness of 3 Shore A. It presents the force values in comparison with pad displacement in Z-direction during a pad pressing on the substrate in the indirect gravure printing process.

All tests are executed in the same air-conditioned laboratory where the material tests were performed (see chapter 4.2.1). Totally, 144 experiments are executed under the described conditions.

Figure 6-5: The force (F) versus the pad displacement (Z) during the pressing of the pad on the substrate for pad 2 with hardness of 3 Shore A is shown here. The black, red and violet colors present the average (Exp.), minimum (Exp._Min), maximum (Exp._Max) of experiment results.

The green color displays simulation (Sim.) result.

Further, the simulation result is displayed in Figure 6-5. It is compared with average values of force achieved in the experiments to validate the simulation result. The comparison shows that the simulation result and the result of the experiments are matched with each other in a highly accurate condition with squared of 0.985. R-squared is the coefficient of determination. In this case, a more appropriate fitting between the simulation result and experiments is achieved while R-squared value is near

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to one. Figure 6-6 shows the simulation results and experiments in different cases which will be discussed in this dissertation. It presents the force values in comparison with pad displacement in Z-direction during a pad pressing on the substrate in the indirect gravure printing process. Black, red, green and blue colors represent the pad models of pad 1, pad 2, pad 3 and pad 4. “Δ”, “*”, “□” and “x” markers on the curves represent the pad hardnesses of 3, 6, 12 and 18 Shore A. Solid and dashed lines indicate the experiments and simulation results, respectively.

Figure 6-6: The pad force versus pad displacement in Z-direction is presented on the curves. Here, the simulation results with solid lines are compared with the experiments with dashed lines. The hardnesses of 3, 6, 12 and 18 Shore A are displayed by “Δ”, “*”, “□” and “x”, respectively. Pad 1, pad 2, pad 3 and pad 4 are shown by black, red, green and blue colors, respectively.

According to Figure 6-6, the deviation between the curves of experiments and simulation results in the pads with model pad 1 is more than other models. The differences between the simulation results and experiments in pad model 4 with hardness of 12 Shore A is the smallest amount and they are fitted with each other.

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Table 6-1 shows the fitting between the simulation results and experiments with R-squared parameter. It is the coefficient of determination. This parameter was described in chapter 4.4 and it is calculated by equations (4-5), (4-6) and (4-7). Table 6-1 structure was designed to make an easier comparison between different pad models and pad hardnesses. In the table, the quantitative parameters are described in a matrix format which each value is related to a special pad hardness and pad model. Columns and rows are related to pad hardnesses and pad model, respectively.

In Table 6-1, R-squared value describes how well the simulation results fit the experiments in each case. The value which is nearer to one, shows more fitting between simulation results and experiments. This is a quantitative parameter to describe the validation of simulation results.

For example, R-squared is 0.995 in the case of pad 4 with hardness of 12 Shore A. In this case, the simulation results can be considered nearly the same as experiments which were performed with this pad during the printing process. Oppositely, R-squared of 0.350 in the case of pad 1 with hardness of 12, shows a non suitable similarity between the simulation results and experiments.

Table 6-1: The accuracy of fit of simulation results with experiments in force-displacement behavior of pads is abstracted here. The R-squared is the coefficient of determination. They are related to pad 1, pad 2, pad 3 and pad 4 with hardnesses of 3, 6, 12 and 18 Shore A.

R-squared 3 Shore A 6 Shore A 12 Shore A 18 Shore A

Pad 1 0.9432 0.7865 0.3507 0.5191

Pad 2 0.9852 0.9791 0.7978 0.8094

Pad 3 0.9864 0.9749 0.9321 0.8988

Pad 4 0.8527 0.9077 0.9951 0.9637

The validation of simulation results was evaluated according to Figure 6-6 and Table 6-1. In this case, the simulation results of the two cases between 16 different cases are not as accurate as others and their R-squared is less than 0.79. They are pad 1 with hardnesses of 12 and 18 Shore A. In other cases, there is a high similarity between the simulation results and experiments. In pad 4 with hardness of 12 Shore A, R-squared value is in the highest value of 0.99. The results of pad 1 are not accurate because of special geometry of the pad. In this case, the pad was designed to observe its behavior

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with minimum possible height. In real case, this geometry never will be used in the printing process. So, it is validated that the simulation represents the real pads behavior.