Mathematical Modeling of the Fibre Orientation Due to Slice Lip Actuators, 1997 Process Control, Electrical & Info. Conference Proceedings

The new type of head boxes with dilution water flow to control the grammage profile allow the simultaneous control of the fibre orientation profile using now the slice lip as profile actuators.

For the automatic control of the fibre orientation, the transfer function between the local slice lip position and the fibre orientation is important. General models show the interdependence of the speed difference between the wire and the jet speed. Especially cross flow components in the headbox and the jet lead to the fibre orientation. Even small cross speed components may lead to large fibre orientation angles, if the wire-jet speed difference is small. From grammage profile control it is well known, that changes in the slice lip position lead to cross flow components. These cross flow are responsible for the coupling between the profile actuators.

To calculate the transfer function between a variation in slice lip position and the fibre orientation profile, a mathematical model has been developed. The module consists of several parts, describing the:

· mechanical deformation of the slice lip due to actuator and including also the headbox deformations,
· the flow within the headbox with regard to the mechanical deformations of the slice lip
· the flow and dewatering on the wire,
· the geometrical model of the fibre orientation due to machine direction and cross direction flows.

The model is simplified in several steps with regard to measured data. Depending on real machine data the calculation of the fibre orientation becomes possible with regard to wire and jet speed.

The paper presents the mathematical model as well as the calculated transfer function between slice lip and fibre orientation. An approximation of possible cross profile control results based on this model is also included.