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On High-Frequency Self-Excitation in Paper Calenders

Brommundt E.

Machine Dynamics Research

2011

Vol. 35, No. 4

5-10

Oscillations at the nip of paper calenders spoil the quality of the paper, cross streaks – bars - occur, the machine will suffer damage. The paper outlines briefly the results of Brommundt (2009). The stability of the stationary motion of a machine with ideally circular elastic rolls is investigated. The paper compression in the nip has a hysteretic characteristic, for the small slip between rolls and paper holds a Coulomb type friction. Two thick-walled hollow cylinders serve as rolls. With respect to polar coordinates, in the unstable, the self-oscillating nonlinear system the third and second order Fourier terms of the noncircular deformation get the largest amplitudes. Thus, the frequency of the selfoscillation lies far above the basic critical frequencies of the rolls in their suspensions. The model can be applied to select stabilizing parameter variations.

A Simple Model for Friction Induced High-Frequency Self-Excitation of Paper Calenders

Brommundt E.

Machine Dynamics Problems

2007

Vol. 31, No. 2

25-45

The model shows the possibility of friction induced high-frequency self-excitation at an ideally cylindrical roll of a paper calender (the ensuing corrugation by wear will amplify and finally govern the process). The basic investigation shows that the geometric and kinematical relations at the nip, together with friction and the material characteristics of the paper, here linearly visco-elastic, favour the excitation of higher order modes of the elastic ring which is taken as roll. The ring is attached to a flexibly mounted hub by a Winkler suspension; (all suspensions visco-elastic). The upper half only of a two roll calender is modelled, and oscillations symmetrical with respect to a horizontal middle plane are analyzed. The oscillations are restricted to the rigid body motions of the system and to a second order Fourier polynomial for the circumferential waves of the bending and the extensional displacements of the ring. Non-linear equations of motion of these 13 degrees of freedom system are established, simplified and, as initial value problem, numerically solved for estimated parameter values. The resulting limit cycle confirms the presumption.