# Production Optimization of Premium Food Can with Distortion Printing under Waving Requirement
## 2 Waving Defect in Food Can Forming
### Distortion Printing in Food Can  
Currently, the premium can production industry, which relies on distortion printing, has elevated its requirements beyond mere engineering functions. The DRD process is essential in the manufacturing of food cans. The industry defines the product code as ABCxDEF. For example, \(307\times 113\) is a can with a diameter of \(307\) (i.e., \(3+07/16\) inch) and a height of \(113\) (i.e., \(1+13/16\) inch). Currently, the factory in this study produces the following DRD food cans: \(307\times 113\) (\(40\%\)), \(211\times 109\) (\(20\%\)), \(300\times 103\) (\(16\%\)), \(300\times 200\) (\(14\%\)), and others (\(10\%\)). This study focuses on the \(307\times 113\) DRD as the case study.  
Achieving a successful food can with distortion printing requires both art and science of forming. For the \(307\times 113\) DRD, an industrial guideline is shown in Figure 3 and includes the following recommendations: To minimize the scrap rate, text should not be placed within \(6\) mm from the bottom edge or within \(8\) mm from the top or seamed edge. Additionally, graphic designs featuring text or straight lines in these areas are susceptible to a distorted display.  
Distortion printing can be analyzed by printing a grid pattern on a flat sheet and then forming into the cylindrical shape of food cans. Grid technology is applied in the food can-forming process to produce new designs and prints. There are four stages in distortion printing: (1) A grid is printed on a flat sheet, and then, a can is formed; (2) the distorted grid is carefully analyzed by measuring the extent of distortion in each square to create a new distorted grid; (3) the new distorted grid is re-printed and then formed again (if it is a bad one, the process is repeated); and (4) once an accepted grid pattern is achieved, the new results are used to create the distorted artwork required by the customer's design. Notably, the uncertainty is not taken into account here. Figure 4 shows the design process on a sheet (36 cans per sheet). Grid adjustment can be performed using two methods: rotation and compensation. Rotation involves adjusting the grid so that the distorted area is free of graphics. Compensation involves pushing or pulling from the original grid. These grid adjustment methods are employed to mitigate waving problems. Figure 4 illustrates the method of correcting the printed image by rotating it from its original orientation. If the method illustrated in Figure 4d is tested and the image quality does not meet the specified standard, the compensation is implemented. Figure 4e demonstrates a method for correcting a printed image by continuously stretching or shrinking it. The image is locally stretched or contracted to compensate for the distorted image in the area requiring correction. In a preliminary trial prior to grid adjustment, the scrap rate is observed to be \(8.33\%\), i.e., \(150\) scrap pieces from a test run of \(1800\) pieces. In a real production after the grid adjustment, the scrap rate decreases to \(1.59\%\), i.e., \(5649\) scrap pieces from \(356,229\) pieces.  
Figure 3: Guideline for design of distortion printing.