# Application of PolyJet 3D Printing in Production of Flexographic Printing Plates
## 2 Materials and Methods  
### Preparation of the Printing Forms Design  
The design of the test plate for 3D printing was prepared in Autodesk Inventor (Autodesk Inc., San Francisco, CA, USA). The test plate included the following fields: solid printed areas (with 100% coverage, also known as apla) and raster fields with 75%, 50%, and 10% coverage (representing shadows, halftones and bright parts of the reproduced image, respectively) (Figure 1b), as well as microlines with thicknesses from 0.1 mm to 0.35 mm in 0.05 mm increments. The distribution of elements on the test plate is shown in Figure 1a.  
In flexographic printing, there is an excessive enlargement of raster points in the highlights on the print due to the pressure applied during the printing process. Also, there is an elongation of the image elements on the printing plate depending on the circumference of the printing cylinder because of the mounting of the flat form on the cylinder surface. To eliminate these changes on the print, their formation should be considered during the manufacturing of the printing plate, and the drawing dimensions should be adjusted accordingly. Therefore, in order to make a CAD model in Autodesk Inventor (Figure 2), a  
Figure 1: The printing plate design: (**a**) the distribution of the elements on the test plate, (**b**) the size of the raster points depending on the degree of surface coverage, (**c**) the comparison of the raster point sizes based on the linearity of the raster, and (**d**) the elongation of the drawing on the printing plate due to mounting on the plate cylinder.  
number of calculations were performed, as follows: percentage shortening of the negative in the printing direction (Figure 1d), radii of single raster points (Figure 1c) for two different printing plate lines, and radii of single raster points in the printing direction (shortened), for two different printing plate lines.  
The percentage shortening was calculated from Equation (1) [37],  
\[SN=\frac{2\pi g}{L}\cdot\text{100\%} \tag{1}\]  
where the following variables are presented:  
SN--shortening of the negative,  
g--thickness of the printing form without substrate,  
L--length of the printed image at one revolution of the printing cylinder.  
The results of the calculations are shown in Table 1.  
Figure 2: The design steps for the printing plate (**a**) the creation of a primer layer of 90 mm \(\times\) 25 mm \(\times\) 1.2 mm, similar to the pre-exposure process in conventional photopolymer plates, (**b**) the creation of a solid area on a test plate with a height of 0.5 mm and an inclination of 65\({}^{\circ}\) with respect to the base layer, (**c**) the preparation of a single raster point with dimensions taking into account the elongation in printing, which was then duplicated the appropriate number of times using a rectangular array operation to create a raster field of 10 mm \(\times\) 10 mm, and (**d**) a finished design of a 3D-printing form with a linearity of 20 kpc.  
The next step in the calculation was to calculate the radii needed for the raster fields of the test plate. The calculations were carried out for two values of printing plate rulings as follows: 20 lpc (lines per centimeter) and 34 lpc, matched to the raster cylinder rulings.  
The results of the calculations are summarized in Table 2. The calculations were made as follows:  
* the area of a single point was calculated, as a percentage of the area of a square with a side length of a fixed raster,
* the radius of the circle of a single point was calculated, using the area of the point,
* the shortened radius of the raster point was calculated (the radius of the raster point shortened by the percentage of the negative shortening).