Ink transfer model and its application in practice (2)

(INK TRANSFER MODELS AND UTILIZATION IN PRACTICAL CONDITIONS)



Ink transfer model



Walker-Fansco model:



According to the transfer experiments of printing inks, Walker and Vansko proposed a semi-empirical formula. It fits well with the previously mentioned ink transfer "S" curve. In the model, the contact of the ink with the material, the absorption and cure of the ink by the material, and the separation of the “free state” ink are taken into consideration. Its mathematical expression is:



Y=A·[b·B + f·(X— Bb)]



Where A = 1 - exp(kx); B = 1 - exp(x/b); Y is the amount of ink transferred by the printing; X is the amount of ink before the transfer; f is the ink separation factor, ie, the "free" ink flow The proportion of printed material; b represents the maximum amount of ink on the material; k is a constant related to the finish of the printed material.



The two exponential values, A and B, are related to the ratio of the area of ​​contact between the ink and substrate and the amount of ink solidified in the pores of the substrate.



According to Rossi and Fan, this model is based on the premise that the ink transfer area is always consistent. In practice, this is not exactly the case. It is related to the geometry, width, and depth of the ink roller meshes. For this reason, they modified the Walker-Fanschow model to add material finish and ink hole area to the ink and printed materials. Contact coefficient of influence.



The significance of the Walker-Fernsco formula is that the ink delivery per unit area of ​​the ink hole is related to the total amount of ink fixed per unit area (bB) of the printing material, the f of the ink separating process, and the ratio of the “free” ink separating.



The other three model formulas:

Uri Berry proposes another mathematical model based on eight sets of experimental data from the National Printing Ink Research Institute. The prerequisites are:



1. The amount of ink on the printing material is very small;

2. Only by physical contact can produce ink adhesion;

3. The transfer process after ink adhesion is uniform;

4. Paper printing surface fluctuations;

5. As the amount of printing ink increases, the ink can reach the bottom of the hole and fill the entire printing plate;

6. If you continue to increase, the ink will penetrate and transfer to the print.



In short, ink delivery is controlled by the following three steps:

1. The ink cures on the surface of the print;

2. The mesh is full of ink;

3. The ink should penetrate the paper.



In the process, the separation of the ink is also accompanied.



The mathematical expression of this model is:

Y1=S1·X + In1(for b1
Y2=S2·X + In2 (for Xmax1
Y3=A + a√X (for X>Xmax2)



Among them, Yi is the amount of ink delivered; X is the amount of ink on the plate.

S1=P + f1·(1-P)

In1= -S*b1

S2=1-(1-f2)*(r-b2)^2/r^2

In2=(p+f1*(1-p))*b2—S2*Xmax1

A=(1-f3)*{P*b2+[(S2-f2)*(Xmax2-Xmax1)+(1-P)*(1-S2)*b2]/(1-f2)-Xmax3}-f3 *b1



Where P represents the surface finish of the paper; Xmax1 is the critical value from the time when the ink cures to full pore fill; Xmax2 is the critical value from the pore fullness until the ink has penetrated; f1 is the ink film between the plate and the pores Separation coefficient at separation; f2 means when Xmax1
This model is a theoretical model and its six parameters can be obtained based on experiments.



New Model for Separation of "Free" Ink

Based on the modified Walker-Fansco model, a calculation model for its ink separation coefficient f is proposed. It is related to the thickness of the ink film and is a positive number, which is closer to the actual situation. Its expression is:



F=f∞ +(0.5 -f∞)·e ^-2f∞X

Among them, F represents the separation factor; f∞ represents the separation factor when the ink volume is maximum; x is the initial amount of ink on the substrate.



The value of 0.5 in the formula is based on the precondition that the two rollers have the same speed, ie, the ink separation is assumed to be distributed in a ratio of 50% to 50%. Of course, this may not always be the case in practice.



This formula is based on the principle of separation asymmetry, that is, when the printing plate ink volume increases, the ink separation ratio also increases.



The revision of the Walker-Van Sike formula:

Many experts later revised the Walker-Fansco formula to better match the actual situation. Among them are the Laurignu, Katuma-Kutu-Odinan formulas and so on. But their principles are the same as the original Walker-Fansco formula. According to Mangaku's experiments, their performance in practice is similar to the Walker-Fansco formula.



Discussion on the model

As mentioned earlier, the mechanism of ink transfer is based on three basic steps. All models are based on this principle. Experimental data are based on measurements. (For example, GATF ink meter, etc.)

The model proposed earlier, such as the Walker-Fansco formula, was only used to describe the mechanism of ink transfer on a letterpress printer. For gravure printing, according to Rossi and Fung's research, this model should be based on the contact area of ​​ink. change. Because in the gravure printing contact area is changed. In the same way, for other forms of printing, the model should also be corrected according to the actual situation.



Perry is the only one who proposes a purely theoretical model. His model fits well with practice. He also published a monograph on the mechanism of ink transfer in the gravure printing of non-absorbent materials. His mathematical formula is very detailed and contains all aspects of the mechanism of ink transfer.



The significance of the model

In describing the actual situation of gravure printing, the ink transfer model is very important.



According to Shou and Fan’s independent study of ink consumption and ink transfer, there is a direct link between them. The ink consumption is related to the print density and print thickness required for the printed material. The ink delivery determines the amount of ink needed for the ink layer of the substrate to reach a certain thickness. For a particular print, if the print reaches a certain optical density, there is a minimum amount of ink required for printing. This content deserves further careful study.



Using the model can save us a lot of research costs and time, and have a good forecast effect

These models can make predictions based on different operating environments and help us choose better printing equipment, printing inks, ink rollers, and printing materials. Correct forecasting of ink transfer can enable us to propose precise ink consumption estimates for specific print jobs and minimize inventory, so that our ink storage can be minimized and at the very best.



According to the model, by changing the specific characteristics of the material in light of the actual situation, we can achieve the best control of product quality. By changing the content of resin in the ink, the size of the pigment, the finish of the printed product, the electrostatic process and other methods, the effective control of printing and ink transfer can be finally achieved.



in conclusion

The ink transfer model fits the actual situation better, it can make us have a best choice for the amount of ink when we reach a certain optical density on the surface of the printed material.



There are three basic steps in the mechanism of ink transfer. People have made many studies on the separation stage of the ink. The speed of the ink roller is an important factor in determining ink separation. With the advancement of technology, the speed of printing presses is getting faster and faster, and the possibility of blurring in printing has become higher and higher. In order to get the best printing effect, printers need to work together with the ink manufacturers to set the best working conditions for printing presses and inks, so that the printing products can obtain the maximum amount of ink while achieving the best printing. The effect and the most economical use.