Mechanics of disk-type false twisting - Part II: Yarn path and yarn inclination angle in a multiple-disk spindle unit

A triple-stack multiple-disk spindle unit is used widely in actual draw texturing processes. In this kind of friction false twisting process, the angle of inclination (angle between yarn path and disk axis) is an important factor that determines yarn tension and twisting torque over the disk surface. This paper proposes a new theory that will give a more precise angle of inclination using differential geometry. The basic assumptions are that the disk profile is represented as an outer surface of a torus, and the yarn path over the disk surface forms a geodesic line. The angle of inclination is calculated by this theory in the actual range of the disk diameter, the radius of the disk edge, and the distance between two neighboring disk axes. The inclination angle obtained by this theory gives smaller values than the angles obtained by previous studies, but the experimental data agree best with the value calculated by this theory. We also explain how to calculate the entry angle (the angle of wrap) and the limiting value of the angle of wrap to guarantee smooth contact of the yarn with the disk periphery. The effect of the profile represented by the radius of the disk on the angle of inclination, and the angle of wrap is also investigated.