Elastohydrodynamic lubrication of soft-layered rollers and tensioned webs in roll-to-plate nanoimprinting

This work presents the development of a numerical model for the elastohydrodynamic lubrication of roll-to-plate nanoimprinting with flexible stamps. Roll-to-plate nanoimprinting is a manufacturing method to replicate micro- and nanotextures on large-area substrates with ultraviolet-curable resins. The roller is equipped with a relatively soft elastomeric layer, which elastically deforms during the imprint process. The elastic deformation is described by linear elasticity theory. It is coupled to the pressure build-up in the liquid resin film, which is described by lubrication theory. The flexible stamp, which is treated as a tensioned web, is pre-tensioned around the roller. The elastic deformation of the tensioned web is described by the large-deflection bending of thin plates equations, considering its non-negligible bending stiffness. A Fischer–Burmeister complementarity condition captures the contact mechanics between the tensioned web and the roller. The governing equations combine in a coupled elastohydrodynamic lubrication model, which is fully described by a set of non-dimensional numbers. These are used in a parameter study to investigate the effect on the pressure and film height distributions. It is shown that the bending stiffness of the tensioned web results in an additional hydrodynamic pressure peak and corresponding minimum in the film height, near the inlet of the roller contact. An increase of the bending stiffness corresponds to a decrease in film height. The numerical results are compared with benchmarks from literature and experimentally validated with layer height measurements from flat layer imprints. Good agreement is found between the numerical and experimental results.