The lateral deflections of webs in roll-to-roll (R2R) process machines can affect the
quality of the manufacturing process. The lateral registration of the web in successive
R2R processes can determine whether a product will function as designed. Herein a
unified theory is presented that explains how imperfections in rollers, their
alignment and length nonuniformity (camber) in webs can affect the steady state
lateral deflection and hence registration. Enhanced understanding of steady
state lateral deflection of webs transiting free spans and rollers will provide
insight for advanced control methods that account for the effects of web
deformation in minimizing registration error. The validated results show that the
lateral deflections can be predicted with closed form solutions when the
slippage between the web and rollers is minimal. In those cases kinematic
boundary conditions will be presented which govern the lateral deflection of
the web. When slippage is present it will be demonstrated the boundary
conditions which govern the lateral deflection must be determined using dynamic
simulation.
Dedicated to the memory of John J.
Shelton
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