Abstract
For the adaption of a roll-to-roll printing method to printed electronics, it is mandatory to increase the register control resolution. Therefore, it is necessary to derive a mathematical model of the register and to develop a controller to reduce register error. A correlation between the machine-direction (MD) and cross-direction (CD) registers was derived by considering both the lateral motion of a moving substrate and the transverse position of a printing roll. By the analysis of the correlation between MD and CD registers, a novel mathematical model of an oblique-machine-direction (OMD) register was derived. The OMD register is more critical in large-area roll-to-roll printing, as the OMD register error is proportional to the width of the substrate. The proposed model can be used to design an effective two-dimensional (2D) register controller that reduces the correlation between MD and CD registers. The proposed mathematical model was validated by numerical simulations and experimental verifications under various operation conditions using a multilayered direct gravure printing machine. The results show that the proposed OMD register model reasonably exposes the MD–CD register correlation.