Dear Jeffrey, You have a really good question. If I remember the
explanation given to me a lot of years ago it has to do with contact
area and approach angle to the roll. I think it has to do with the
force moment getting higher as the contact area gets smaller. You
may have seen rolling mills used for thin material rolling that back
up a small diameter contact roll with larger diameter anti deflection
rolls. The simplest of these is called a four high mill. I have seen
pictures of 30 high mills with very small diameter contact rolls that
are backed up by two larger diameter rolls that are still not large
enough to resist deflection so they are backed up pyramid style by
three and then four and finally five rolls, each set progressively
bigger. This way the large rolls keep the whole set flat and the
small rolls have small approach angle beneficial for making ultra
thin strip. If I add correctly that would be 15 rolls on the top and
15 on the bottom.
I don't have any text here that I can refer to, but I would start to
look for more on this in The Metals Handbook published by
the American Society for Metals (ASM). I think they have changed
their name to American Society for Materials.
Now for the practical side for us jewelers. First of all I didn't
think my argument through as carefully as I should have. In my mind I
started with the thought that material strength needed to be
considered when analyzing the rolling mill and one should not
automatically assume that bigger is better. My point, not very
eloquently made, was that smaller and stronger might be better. In
theory the 200 should be able to make thinner strip, but from a
practical standpoint, I don't know how much thinner a strip can be
rolled from a roll 200 mm vs. 250 mm and both may be able to get the
material thinner than needed.
As for the heavy duty mill you worked with, you are right, there are
other places where a roll can deflect. The bearings and the H frame
must react to every force exerted on them and the stronger the
better. The effect of bearing deflection would be scalloping with
roller bearings (this can also be caused by the face roll not being
concentric with the axle of the roll) and gap opening for bushings.
Frame stretch would open the gap and this could be parallel if both
sides move evenly or wedge if one side moves more than the other.
The Bell Group/Rio Grande