• Paper calenders;
  • self-excited vibrations;
  • paper machinery;
  • stability analysis;
  • paper modeling.


The manufacturing process of paper machines consists of several steps to produce high quality papers. This is done by sequentially lined-up machines including the head box, the drying sections, the finishing part and the wrapping systems. In the finishing part, the rollers of the paper calender compress the fibrous material involving viscoelastic and plastic deformations. Modern calenders are composed of several roller pairs, each consisting of a soft and a hard roller. The homogenization of the paper density and the refinement of the paper surface is achieved by the compression in the roller pairs. While very high values for the plastic strain occur in the first roller pair, the plastification decreases for the subsequent pairs. Therefore, the force distribution and the occurring vibrations can deviate significantly between the roller pairs. Two main vibration problems are observed in paper calenders caused by the contact and the orthotropic behavior of the paper: wear-induced corrugation on the surface of the soft rollers and sudden instabilities going along with high vibration amplitudes. In this paper the main focus is placed on a simplified modeling of the paper plastification during the calendering process. The restoring forces are non-smooth due to the plasticity and additional considerations have to be included for the derivation of the stability problem.