MATHEMATICAL MODELING OF OVER-END YARN WITHDRAWL, AND THE DEVELOPMENT / DESIGN OF A DEVICE FOR UNIFORM UNWINDING TENSION

Abstract: It has been observed over the years that yarn tension during high speed over-end unwinding from a helically wound stationary package is highly non linear (1). Each yarn element during unwinding performs a complex motion that involves a movement along the yarn axis and rotation about the package axis. Parameters that affect the yarn tension are linear yarn density, unwinding speed, package diameter, balloon profile, and specific yarn winding density of the cone or cheese. This paper analyses mathematically the influence of the above stated parameters at the guide eyelet on yarn unwinding tension. On the basis of the model it proposes a cost effective mechanical device for tension variation control where a movable guide eyelet is used. The proposed device helps to minimize tension variation during unwinding and to obtain more or less constant tension, which definitely improves the quality of the package prepared from cones or cheeses ( for example a warp beam). The concept behind the proposed system is to move the guide eyelet with respect to reducing cone or cheese diameter according to the proposed mathematical model. This will invariably affect the uniform unwinding tension, which also improves the quality of subsequent processes such as warping, sizing, pirn winding and processes associated with package dyeing