**4. Experiment**

By manufacturing the optimized barrel roller, we were able to verify its compensation performance. For a span length of 200 mm, the average deviation was 8.54 μm for the conventional roller and 4.42 μm for the optimized barrel roller. This represents a compensation of approximately 48%. Under the same conditions as in the experiment, FEA produces a compensation performance of 85%.

#### *4.1. Experiment for Verifying the Performance of Barrel Roller*

We conducted an experiment to evaluate the compensation performance of the optimized barrel roller. The optimized barrel roller was a barrel-shaped A3B3C1 combination; the thickness gradient of the skin was 8 mm, the total diameter of the roller was 60 mm, and the elastic modulus of the shell was 2.85 MPa (Figure 13).

**Figure 13.** Optimized barrel roller fabricated with final design parameters.

To evaluate the performance of the barrel roller, we conducted a comparative experiment by replacing the fixed-end roller with the barrel roller, as shown in Figure 14. The load-end roller was a conventional roller. Reference marks were also placed by a laser; the relative displacement of the laser marks was measured with a vision camera, and the strain was calculated. In this experiment, we used 28 marks—14 marks are close to the optimized barrel roller (fixed end) and 14 marks near the conventional roller (load end). The web used in the experiment was a PET film (Mitsubishi Inc. O321E188) with a width of 160 mm and a thickness of 188 μm. The experimental apparatus is shown in Figure 15.

**Figure 14.** Schematic of web strain measurement (top view) with a barrel roller.

**Figure 15.** Experimental setup for strain measurement: linear motion (LM) guide and four vision cameras.

Tension in the film was engaged with dancer rollers and measured with load cells at both ends of the roller at the load end. In the FEA, the load condition was assumed to be 10 MPa; however, in the experiment, the maximum tension was limited to 5 MPa due to the load limit of the dancer roller. Since we assumed that the deformation of the web and skin occurred only within the elastic region, a linear relationship between the strain and tension was assumed.

The vision cameras were positioned 50 and 150 mm away from the central axis of the roller and the web was transferred. When a reference mark entered the field of view of the vision camera, the transfer of the web was stopped and the position of the mark was measured. To measure the strain, a pair of reference marks at 100 mm intervals in the MD was pictured on the web under a load of approximately 3 MPa, and all reference positions were measured first. In the next step, the tension was increased to 5 MPa, and the positions of the marks were determined to calculate the strain. The procedure was repeated three times; marks #6 to #9 could not be measured due to mechanical interference between the vision cameras.

The experimental measurements of the strain deviation in the MD are shown in Figure 16 and Table 8. Figure 16 shows the relative displacements in the MD under tension condition at each reference mark. Table 8 compares the deviation in the relative displacements in the MD of each experiment. The mean deviations for the conventional and barrel rollers were 8.54 and 4.42 μm, respectively; thus, the deviation of barrel roller was 48% lower.

**Figure 16.** Comparison between relative displacements of conventional and optimized barrel rollers. The laser pattern number is an index in Figure 14. The spacing between the laser pattern numbers is 10 mm.

**Table 8.** Deviation of relative displacement in each experiment: Conventional versus optimized barrel roller.


**Table 9.**

the same tension conditions as the experiment.

Mechanical

Silicon rubber (skin)

> Web (PET)

 properties applied to FEA to simulate the MD strain deviation of the web under

#### *4.2. Comparison of Experimental and FEA Results*

In the DOE-based FEA, the tension was 10 MPa. However, the experiment was conducted under 5 MPa of tension due to the maximum load limitation of the dancer roller. In addition, reference markings for measuring the MD strain deviation were already engraved under a tension of 3 MPa. This is because the web is transferred to the patterning section. Therefore, in the verification experiment, the reference position of each mark was measured under 3 MPa of tension, and the strain was calculated by measuring the position of the mark after increasing the tension to 5 MPa. To compare the MD strain deviations of the experiments and FEA under the same conditions, an FE model with a tension of 5 MPa was constructed. In the 200 mm span, the printing lines were set at distances of 50 and 150 mm from the contact point of the roller and the web. The mechanical properties used in this FEA are shown in Table 9. Figure 17 shows the FEA results of the strain distribution in the MD for these conditions.

**Young's Modulus Mass Density Poisson's Ratio E (GPa)** ρ **(kg**/**m3) -** Roll (aluminum) 71 2,770 0.33

> 1,200

> 1,320

 0.5

 0.34

 0.00285

> 3.5

**Figure 17.** Comparison of FEA between the existing roller and barrel roller derived by calculating the MD strain distribution under 3 MPa of tension and then changing the tension to 5 MPa.

The strain deviations of the conventional and optimized barrel rollers were 0.00357% and 0.0005%, respectively. For the FEA model, the relative displacements were 7.14 and 1 μm, respectively. Based on these results, the compensation performance was approximately 85%.

There are a few explanations for the mismatch between the results of the experiment and the FEA. The reference marks were not placed exactly 50 mm from the central axis of the roller in the actual experiment. Additionally, uniform tension could not be applied with the dancer roller. Moreover, the reference marks may not have been symmetrically arranged around the center of the CD of the web, the laser mark array and the central axis of the rollers were misaligned, and the properties applied in the FEA were not perfectly accurate.
