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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.