# Modeling of the compression of coated papers in a soft rolling nip

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## Abstract

An analytical model is developed for the compression of coated substrates in a soft rolling nip formed between a hard roll and a soft covered roll. The coating layer, substrate, and soft cover are modeled as a stack of three layers that are compressed jointly while passing through the nip. Material models have been adopted separately for each of the three layers and were combined together according to the thickness of individual layers. In this study, the substrate is considered to be a viscoelastic–plastic material and is represented by a modified solid element while the coating layer is assumed to be elastic and the soft cover material is approximated by a standard Maxwell model. A strain function is derived for the compression of substrate in the nip that appears to be a parabolic function of time. Substrate compression in the nip and its subsequent relaxation are calculated by solving a set of differential equations that describe the coating, substrate, and soft cover deformations. This model is used to study the soft-nip calendering of coated papers. Examples of numerical modeling that demonstrate the paper deformation and stress profiles in the nip are presented. In addition, the effects of paper and cover properties as well as calendering parameters on the dynamics of paper compression are discussed. Finally, a comparison of the modeling results is made with the experimental data.

## Keywords

Coating Layer Stress Profile Line Load Coated Substrate Maximum Compressive Stress## Notes

### Acknowledgements

Financial support from NSERC Strategic Grant Program and Surface Science Research Consortium at the University of Toronto is gratefully acknowledged. In addition, the authors thank Dr. Jörg Rheims for providing the calendering data and Mr. Peter Angelo for his help with editing this article.

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