Vibration Suppression of an Axially Moving Web in a Multi-Span Roll-to-Roll Microcontact Printing System

Background The focus of this work was to investigate the vibration suppression of an axially moving web traveling between multiple rolls. Method Web axial tension and axial speed, decisive parameters in the equation of motion, that describe system dynamics, are rigorously obtained by considering the rolls-web coupled system's dynamics. The proposed control method is based on imposing a suitable boundary condition and applying control torques at rolls, such that the vibration energy at the end of web decays. The non-linear dynamic equation is realized by applying the Hamilton's principle. Using a finite difference and state space approach, the partial differential equation of motion is converted into a system of coupled first-order ordinary differential equations (ODE's) in time by eliminating the spatial variable. Results It was shown through numerical results that by imposing a boundary condition, the vibrational energy decayed, preventing the web excessive vibrations. The effect of dimensionless speed showed a significant decrease in the amplitude and the transverse displacement reduction was more prominent as the dimensionless speed was increased. Numerical simulations are also backed by experiments, which showed a significant web oscillation reduction. Conclusions Results from both the experiments and numerical simulations show that the proposed method can effectively suppress the vibration of the axially moving web, thereby protecting the web from excessive oscillations.