Method for printing on absorbent printing material using inks and dampening fluids

1. A method for printing on an absorbent printing material using inks and dampening fluids, wherein both the inks and the dampening fluids contain water as a solvent and a dampening fluid is colorless, wherein an ink printing machine having at least two ink print heads and at least one dampening fluid print head is provided, wherein the at least two ink print heads apply an ink image to be printed to a front side of the absorbent printing material and the at least one dampening fluid print head applies a dampening fluid image, to be printed to the front side of the absorbent printing material, thus reducing or avoiding water-related cockling of the absorbent printing material, and wherein a computer is provided, which method comprises the following steps of:

a) providing the ink image to be printed onto the front side of the printing material;

b) calculating n different color separation matrices of the ink image with n ∈ and n≥2;

c) calculating n ink amount matrices A n from the n different color separation matrices of the ink image;

d) calculating a total ink amount matrix A as A=A 1 +A 2 + . . . +A n ;

e) calculating a matrix B i,j as B i,j =G*A for every element A(i, j) of the total ink amount matrix A, by multiplying the total ink amount matrix A with a provided weighting matrix G, and determining a maximum Max i,j of a matrix B;

f) calculating a dampening fluid amount matrix C as C(i,j)=MaxB i, −A(i,j);

g) calculating the dampening fluid image to be printed onto the front side of the absorbent printing material from the dampening fluid image matrix C;

h) screening the n different color separation matrices of the ink image using a raster image processor;

i) screening the dampening fluid image using the raster image processor;

j) printing the ink image; and

k) printing the dampening fluid image.

2. The method according to claim 1 , wherein the n different color separation matrices of the ink image are calculated as CMYK or CMYKOGV matrices.

3. The method according to claim 1 , which further comprises calculating the n ink amount matrices A n , using a relationship T 1 between intensity or optical density and layer thickness.

4. The method according to claim 1 , wherein a respective weighting g 1 n of the n ink amount matrices A n is factored in when the total ink amount matrix A is calculated.

5. The method according to claim 4 , wherein in terms of progression of values of elements G(i,j) thereof, the weighting matrix G is provided as a matrix that is cone-shaped at a center and filled with zeroes at margins.

6. The method according to claim 1 , wherein a weighting g 2 of the maximum MaxB i,j of the matrix B and the elements A(i,j) of the total ink amount matrix A in accordance with a respective water content of the dampening fluid and the inks is factored in when the dampening fluid matrix C is calculated.

7. The method according to claim 1 , which further comprises calculating the dampening fluid image using a provided relationship T 2 between intensity and layer thickness.

8. The method according to claim 1 , which further comprise:

repeating steps a)-g) for a further image to be printed onto a back side of the absorbent printing material;

comparing the ink image or a dampening image value of the front side image and a corresponding back-side value of ink or the dampening fluid image on the back side at every printing material location to be printed on; and

transferring a greater value obtained in a comparison for one image to a corresponding other image.

9. The method according to claim 1 , wherein the dampening fluid print head has a lower print resolution than the ink print heads.

10. The method according to claim 1 , wherein the computer is provided to carry out calculating, determining, and comparing steps.

11. The method according to claim 1 , wherein:

the dampening fluid image surrounds; and

the ink image is an RGB image.

12. The method according to claim 3 , wherein the step of calculating the ink amount matrices A n using the relationship T 1 between the intensity or the optical density and the layer thickness uses a Tollenaar curve.

13. The method according to claim 7 , which further comprises calculating the dampening fluid image using a Tollenaar curve or an inverse thereof.