On-line contactless measurement of the elastic modulus of a moving sheet by ultrasonic method

Abstract

There is still a strong interest in the paper industry for a contactless method that would allow the measurement of the elastic modulus of paper and of the anisotropy of this modulus in the sheet plane. A contactless method is presented that enables the measurement of the transmission coefficient of sound through a paper sheet, in the frequency range 200– 800 kHz, for incidence angles between −66 and +66. These measurements can be performed on a moving sheet at velocities in the same range as those observed on a paper machine. From the state equation of plate waves, the possibility to calculate the elastic modulus of paper was demonstrated by using only the equation of the first antisymmetric mode, without neglecting any term of it, contrary to what is commonly used in the literature. This model fits very well with measurements made and leads to consideration of the development of an on-line version for use on industrial paper machines.

Observer-Based Estimation of Modulus of Elasticity for Papermaking Process

“…The modulus of elasticity (E) is a physical parameter that characterizes the deformation (elongation) of the paper web under stress (force per unit of cross-sectional area). This parameter provides important information related to the ultimate breaking strength of the sheet and indirectly its moisture content [1]- [8].…”