chapter  3
Friction force in friction field
Pages 3

In the drafting zone, a fibre is subjected to a friction force due to contact with other fibres and rollers. For simplicity, we presume a fibre to be straight, inextensible and move along its length with the surface velocity of the rollers. Furthermore, it is also assumed that the contact of a fibre with surrounding fibres and rollers is continuous and their pressure is normal to the fibre. Then the total friction force over the fibre developed in a particular friction field is given by

where x t is the trailing end and xi is the leading end. There are six different possible arrangements, as shown in Figure 9, for a fibre in the friction field. When fibres are in the friction field, the integration limits are from the tailing end to the leading end. If fibres are entirely out of the friction field, then no possible friction force can be developed in the friction field. In this case, the fibres keep moving due to the adhesion forces with the adjacent fibres. The magnitude of the adhesion force is mostly related to the static coefficient of the friction [39,40].