Optimal velocity profile design for transport of viscoelastic webs in roll-to-roll manufacturing

In this paper, we consider the problem of optimal velocity profile design to minimize transverse vibrations (web flutter) for moving viscoelastic webs. The web is modeled as a membrane considering the viscoelastic behavior of web materials. Governing equations for the in-plane and out-of-plane motions are derived using extended Hamilton's principle and the Galerkin method is employed to obtain numerical solutions for the equations of motion. An optimal control problem is utilized to obtain the desired web velocity profile that minimizes the transverse vibration energy. Numerical simulation results of the approach show that the new velocity profile achieves suppression of transverse vibrations. The proposed velocity profile is compared with the conventional velocity profile which is implemented in many industrial roll-to-roll machines. Comparative results are presented and discussed in the paper in addition to the development of governing equations of motion for viscoelastic webs.