You have all the parameters and loads for the design, all you need is the cookbook recipe to design it, right? Why keep all of those important design considerations secret, but then ask how do I design this thing that you guys know almost nothing about? It’s a simple beam btwn. the bearings, with a drastically varying cross sectional stiffness and shape, with the center 14" loaded with a uniform line load, centered on and aligned with the shaft axis, plus some torsional and shear loading. The thin wall thickness will give you fits and a secondary deflection.
Are you squeezing the water out of a extruded shape of pulp to end up with a fairly dry, and firm 14" wide strip of paper that’s .03 - .06" thick. How do you form the edges of this strip or prevent the extruded shape from expanding laterally when going through the rollers? What is the compressive strength of the .06" paper strip material, right out of the rollers? Where did you get or how did you arrive at ~200psi?
The rollers are both driven, and at the same surface speed, right? So you don’t introduce a shearing force into the paper. You say 16" long and 8" O.D. with thinnest wall possible. How do you know the roller material before you do the design? Why 8" dia. and as light as possible? Why not 6" dia. and much thicker wall? You get a much better roller surface and a stiffer roller. Then how do you put ends on this mechanical tubing, which are fatigue resistant, and provide for end bearings and a drive system, and won’t defect to much? I venture to guess that you will end up better off buying two pieces of a high quality 7" round stock, and machining your rollers out of them. Or, go for thinnest tube wall possible and start a fatigue testing program, and get paper which is .06" at the center and .04 at each edge. What’s the reason for the thinnest possible pipe walls, because this fatigue testing program could get pricy.