Most of the old stacks of sheets still in use today were for polystyrene or other easily deformed polymers. In these stacks, the top roll was generally smaller in diameter to facilitate easier and safer â€œthreadingâ€ of the line (Fig.1). Since the polymer contact time with the upper roll is only a few inches, the smaller roll causes virtually no cooling.

But nowadays, with the conversion of many sheet products to polypropylene, this has resulted in many stacks of rolls having unacceptable deflection of the rollers, resulting in a sheet that is curved. Polypropylene requires greater calender nip force due to its viscoelastic properties as well as its tendency to increase its viscosity under certain stress levels.

**FIG. 1** In old-fashioned piles designed for PS, the top roll was generally smaller in diameter to make line “stringing” easier and safer.

Adding a larger diameter top roll to an existing roll stack requires very significant machine modifications; and if the center roll also deflects, although to a lesser extent, the larger top roll only reduces – but not eliminates – the problem. An approximation of the separation force causing the rollers to deflect in a roll stack is shown in the following calculation:

*Pounds of separation force in toe-in per inch of length: PLI = G**[3**Âµ(2**Ï€N)R ^{2}*

*]/ 4H*

G depends on the size of the bank and the power law coefficient, but for the approximation you can only use the power law coefficient, because the bank varies from day to day, just like its viscosity.

Âµ is the low shear viscosity at melting temperature.

N = rpm / sec

R is the roll radius

H is the rolling gap

The PLI in the nip is therefore proportional to the power law coefficient of the polymer. The power law coefficient for PP is 0.38, while HIPS is 0.28. This means that it takes 35% more force to maintain the roll position with PP than with HIPS. Note that the separation force is divided by four times the nip height, which means that the deflection increases with the decrease in the thickness of the sheet.

So, the problem of excessive deformation mainly occurs with thinner PP sheet. With most thin sheets, the shear rates are generally low in the roll nip, so there is little shear thinning to consider except at very high line speeds. The roll radius is square in the calculation, so it’s easy to see how the roll diameter solves deflection issues.

The calculation illustrates how the variables contribute to the force of separation. Taking the width of the bank multiplied by the separation force per inch equals the total separation force. This can then be factored into standard beam calculations to determine the roll deviation. The best way to determine the separation force is always to lower the closing pressure in the cylinders until the upper roll â€œfloatsâ€, as this takes every variable into account.

Adding a larger diameter top roll to an existing roll stack requires very significant machine modifications.

One possible solution is to use a top roller that deflects in the opposite direction. Even if both the top and the middle are deflected, the reverse bending top roll can accommodate this to maintain a parallel roll gap. A schematic of this design is shown in Figure 2. There were many such reverse deflection rollers manufactured for several years, which have been in continuous use since 1996; but New Castle Industries, the company holding the patent, ceased its roller business and little, if any, was manufactured after 2004. The original patent expired in 2013.

**FIG 2** In reverse deflection rollers, the top roll deflects in the opposite direction. Even if both the top and the middle are deflected, the reverse bending top roll can accommodate this to maintain a parallel roll gap.

In the design of the reverse deflection roller, a center shell and a center supporting the cooling surface off the center shaft are added so that it deflects in the opposite direction. If the design of the opposite roll (middle) is known, its deflection can be exactly matched to the opposite roll by changing the thickness of the shells. Cooling can be designed to â€œone end, exit the otherâ€ or to enter / exit the same end. By making the center shaft strong, almost all of the shaft deflection is eliminated.

I remembered the reverse fold design when I was contacted by a sheet processor that has been using it for about 20 years and wanted some to be built for additional sheet rows. This can solve your roll deflection issues at a much lower cost than converting your existing stack of sheets or purchasing a larger stack.

**ABOUT THE AUTHOR: Jim Frankland** is a mechanical engineer who has been involved in all types of extrusion processing for over 50 years. He is now President of Frankland Plastics Consulting, LLC. Contact [email protected] or (724) 651-9196.