Boundary conditions for lateral deformation of webs transiting rollers in roll-to-roll process machines

Abstract

The lateral deformations 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 deformation and hence registration. Enhanced understanding of steady state lateral deformation 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 deformations can be predicted with closed form equations. In some cases the boundary conditions which are integrated into these equations must be determined using dynamic simulation.