The Calendering Creep Equation – A Physical Model

Abstract

The modelling of the calendering process has been largely empirical, resulting in “creep” equations which relate the finished paper properties to calender parameters. Such modelling has the utility of optimizing calendering configurations for the attainment of a desired paper finish. This approach demonstrates the limitations of machine calendering and other alternatives to reach higher levels of surface finish are suggested.

This study endeavours to establish an understanding of the physical basis for the form of the calendering creep equation. A simple physical model of calendering has been developed which allows at least the qualitative prediction of various calendering effects. The physical model of paper compression is based on the non-Hookean behaviour of paper under compression which is known to arise from the statistical distribution of the number of fibers in a paper web. Elastic constants associated with the exponential stress-strain relation for paper determine the dependencies of caliper reduction on moisture, temperature and fiber processing. A simple viscoelastic model suggests that the dependencies on moisture and temperature may not be as autonomous as they appear in the usual forms of the creep equation. This observation is corroborated by experimental data obtained on pilot laboratory calenders.