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Characterization of the formation of base sheet paper using spectral moments determined from time-series models

Published online by Cambridge University Press:  12 April 2006

Warren R. Devries  and
S. M. Wu
Warren R. Devries
Affiliation:
Department of Mechanical Engineering, University of Wisconsin, Madison Present address: Department of Mechanical Engineering, University of Michigan, Ann Arbor.
S. M. Wu
Affiliation:
Department of Mechanical Engineering, University of Wisconsin, Madison
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Abstract

The fibre distribution in a sheet of paper, referred to as the formation, is largely the result of turbulence, a stochastic process. Continuous time-series models developed from discrete light-transmission profiles are used to characterize formation. The models are used to obtain explicit expressions for the spectral moments of the profiles. From the moments, estimates of two characteristic lengths of the fibre distribution can be obtained and are interpreted as the average and largest flock size. These lengths are used to develop an index for evaluating the formation of four samples of base sheet paper. The results of this characterization agree with other methods, but this technique has the advantage of providing a physical interpretation of the index.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 82 , Issue 2 , 7 September 1977 , pp. 261 - 272
Copyright
© 1977 Cambridge University Press

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References

Åstöm, K. J. 1970 Introduction to Stochastic Control Theory. Academic Press.
Norman, B. & Wahren, D. 1972 A comprehensive method for the description of mass distribution in sheets and flocculation and turbulence in suspensions. Svensk Papperstidning 75, 807–818.Google Scholar
Pandit, S. M. & Wu, S. M. 1975 Unique estimates of the parameters of a continuous stationary stochastic process. Biometrika 62, 496–503.Google Scholar
Parker, J. D. 1971 Development of smaller scale structures in headbox design. Australian Pulp Paper Indust. Tech. Ass. 25, 185–193.Google Scholar
Parzen, E. 1972 Some recent advances in time series analysis. In Statistical Models and Turbulence, pp. 470–492. Springer.
Reiner, L. & Wahren, D. 1970 The characterization of flow from the headbox of a paper machine. Svensk Papperstidning 74, 225–232.Google Scholar
Taylor, G. I. 1935 Statistical theory of turbulence. Proc. Roy. Soc. A 51, 421–479.Google Scholar
Wu, S. M. 1976 Dynamic data system, a new modeling approach. A.S.M.E. Paper 76-WA/Prod-24.