2D Case 2: Roller Deflection

Rollers deflection has two variations:

Dual-end supported rollers (i.e., like a bridge supported from both sides of the river or valley).
Cantilevered supported rollers (i.e., like a diving board, supported from one side, but unsupported on the other end).

In dual-supported rollers, the bending and deflection of the roller shell will have the greatest effect on the web.

In cantilevered rollers, deflection of the shaft or cantilevered support beam is most important.

In each case, deflection is reduced by either reducing the load on the bending element or increasing bending resistance.

Solutions

Reduce the loads creating roller or roll deflection: decrease tension, decrease nip loads, reduce roll weight (i.e., reduce width, diameter, density, core weight).
Increase roller or core diameter.
Increase roller or core wall thickness.
Reduce roller or roll face width.
Change to a roller shell, core, or core shaft material with a higher modulus.
Change the roller internal design to have greater bending stiffness.
Optimized bowed roller curvature, wrap angle, and orientation.

Reduce the loads creating roller or roll deflection: decrease tension, decrease nip loads, reduce roll weight (i.e., reduce width, diameter, density, core weight).
Increase roller or core diameter.
Increase roller or core wall thickness.
Reduce roller or roll face width. (Cantilevered rollers and shafts are best used below a 5:1 width/diameter ratio.)
Change to a roller shell, core, or core shaft material with a higher modulus.
Mount a dual-end supported roller on a high stiffness cantilevered beam.