The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc.
Aalto

Contact Mechanical Model for Winding Nip

Marko Jorkama

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Engineering Physics and Mathematics for public examination and debate in Auditorium E at Helsinki University of Technology (Espoo, Finland) on the 12th of January, 2001, at 12 o'clock noon.

Dissertation in PDF format (ISBN 951-22-5703-3)   [1072 KB]
Dissertation is also available in print (ISBN 951-666-559-4)

Abstract

A winding simulation model predicting the internal stress state of a wound roll would provide an indispensable tool for the optimal selection of the winding parameters and, above all, a fast way to design new winding concepts - such as winding drum covers and winding geometry. Hence, the nip-induced stresses and nip-induced tension are of the outmost interest to the manufacturer of the winding apparatus. In this thesis, a rigorous contact mechanical model for the winding nip is presented. Under the assumptions of the linear elastic web and paper roll material and compliant winding drum, the indentation, stick and slip equations are derived. The wound-on-condition, a mathematical statement for the initially free sheet becoming finally a part of the roll, is presented. A variant of the Panagiotopoulos Process is introduced as a solution procedure and numerical results are presented. An invariant condition is derived and, hence, the number of independent winding parameters is reduced from three to two. In the numerical part of the thesis, the basic mechanism of the nip-induced tension is presented and the following items are studied: the influence of the winding force, the layer-to-layer friction coefficient, the wound roll and winding drum radius, drum cover compliancy and the elastic constants of paper on the nip-induced tension. The calculated results obtained are shown to comply well with the experiments and literature.

Keywords: elastic contact, winding, paper, nip-induced tension, orthotropic, elastic half-space, elastic cylinder, elastic thin sheet

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© 2001 Helsinki University of Technology

Last update 2011-05-26