Paper bending stiffness and web tension measurement from a running web using a vacuum and computer imaging

A novel method for measuring the bending stiffness of paper online during manufacturing is introduced. The method uses photometric stereo imaging to detect the shape of the deflection surface caused by a controllable pressure difference over the paper’s surfaces. The hardware for the measurement is based on a combination of two existing sensors, which has accelerated and facilitated the development of the implementation. The deflection and loads are tied together by the governing differential equation for the bending of an orthotropic elastic plate with selected simplifications. An approach to resolve material parameters and in-plane loads without knowledge of traditional boundary conditions is suggested. The presented method was tested in a paper mill during manufacturing. For bending stiffnesses measured online, correlation coefficients 0.88 and 0.92 were obtained compared to state-of-the-art laboratory measurements. However, the results gained from a moving web are noisy and the data requires correction of the slope and an off-set. Although several issues remain to be resolved before the method can be considered as an accurate measurement for industrial use, the theoretical background, the performance of online implementation, and the results are promising. Possible causes for the observed discrepancies and the future development of the method are discussed.