Eigenvalue Analysis of Oscillatory Variable State Paper Winder

Winding is a paper finishing process, in which the full paper web is longitudinally cut and wound in narrower paper rolls to fit later to printing machines. The quality of the paper roll is measured in terms of uniform roundness and axially symmetric internal stress and stiffness distribution. Unfortunately dynamic effects disturb winding process so that out-of-roundness shape error profiles may accumulate to the rolls. The reason for this phenomenon is mechanical oscillation, in which the set of rolls and the three winding drums are in relative motion in normal direction of their rolling contact plane. The time evolution of this process is extremely complicated since the roll size as well as contact conditions and running frequencies are changing during the complete process. To avoid unwanted resonance crossings the system eigenstates have to be as first step analyzed and compared with the roll speed harmonics at each roll diameter. This analysis is carried out using linearized spring-mass model, whose parameters are updated according to the roll growth. The spring elements represent the local stiffnesses of roll-drum contacts in both normal and tangential directions, the effect of latter ones being actually a novel element introduced in this analysis.