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.