Could you direct me to where I could find these approximate calculations?? I'd like to do the same on my press.
The method I used is based on the solving of the simultaneous equations of the nip equations. The idea is that one makes an equation for each nip. The ink films going into the nip from the surfaces of each roller are added in the nip and then split with a 50%-50% split. So a general nip equation would look like :
a + b = 2c where a and b are the ink films going into the nip and c values of the ink going out of the nip.
For a roller train with a lot of nips, there might be more than 15 equations to solve. One can do this manually but that can be quite frustrating since it is easy to make a mistake. It is the same method that is used in high school math for solving a few simultaneous equations. I have used a computer with a math program to do my solutions. This method is mainly used for solving the 100% coverage condition.
Press simulation programs can be used to see how non 100% coverage conditions will run. From these one can see that patterns in the ink film thickness are constantly changing on rollers as the press runs. These programs work by making incremental rotations of the roller train and calculating the ink film splits. As the program runs the ink films are established.
These kinds of programs are very good for investigating transients. The only problem with these programs is that they assume a positive ink feed. If the press would have a positive ink feed, then their performance would be more in line with these simulators.
Not sure where you can get specific info on these methods. I know there was a TAGA paper that was specifically aimed at the first method above and was written in 1984 I think.
If you want to see how the ink film increases as one goes up the roller train, make a simple roller train that consists of only a chain of rollers. Blanket cylinder, plate cylinder, one form roller, then a stack of rollers on that.
Assume 100% coverage and a 50-50 split.
Start from the paper with 1t on the paper and 1t on the blanket returning to the plate after the blanket paper nip.
On the blanket going to the paper blanket nip there would be a ink film of 2t. 2t = t + t
At the plate blanket nip one would have t + 3t = 2t + 2t . At the form roller plate nip one gets
2t + 4t = 3t + 3t
At the form roller to distributor roller nip one gets 3t + 5t = 4t + 4t
Keep going up and you can see that the ink film increases at each step but the ink transfer at each nip is the same. In this case at each nip only 1t of ink is transferred to the next roller.